Trading Cloud Computing Stocks Using SMA

Abstract

As cloud computing adoption becomes mainstream, the cloud services market offers vast profits. Moreover, serverless computing, the next stage of cloud computing, comes with huge economic potential. To capitalize on this trend, investors are interested in trading cloud stocks. As high-growth technology stocks, investing in cloud stocks is both rewarding and challenging. The research question here is how a trading strategy will perform on cloud stocks. As a result, this paper employs an effective method—Simple Moving Average (SMA)—to trade cloud stocks. To evaluate its performance, we conducted extensive experiments with real market data that spans over 23 years. Results show that SMA can achieve satisfying performance in terms of several measures, including MAE, RMSE, and R-squared.

1. Introduction

Simply put, cloud computing is the delivery of computing services over the internet. It has become the backbone of modern IT infrastructure. Cloud computing is an evolutionary technology that has transformed a large part of the IT industry [1]. It estimates that 67% of enterprise IT infrastructure and software spending will be for cloud-based offerings by 2020 [2]. According to National Institute of Standards and Technology (NIST), cloud computing is “a model for enabling ubiquitous, convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, servers, storage, applications, and services) that can be rapidly provisioned and released with minimal management effort or service provider interaction” [3].

Cloud computing approaches the dream of computing as a utility by offering hardware and software as services. With virtualization technologies, cloud computing can provide an “infinite” amount of computing resources on demand, which is unprecedented in IT history. Cloud computing adopts the “pay-as-you-go” model. It allows users to pay for the use of computing resources on a short-term basis and release them when they are no longer used. As it eliminates large upfront expenses in hardware and expensive labor costs for maintenance, cloud computing is beneficial to small- and medium-sized enterprises, as well as large-sized enterprises. Compared with other models, cloud computing is easier to access and use, cost-efficient, and environmentally sustainable [4].

Serverless computing has gained significant attention in industry and academia over the past 5 years [5]. It is a new cloud computing paradigm that is going to be the “next big thing” of the next decade [2]. It is emerging as a compelling paradigm for the deployment of cloud applications as enterprise application architectures shift to containers and microservices. Serverless computing provides a simplified programming model for creating cloud applications that eliminate most operational concerns. Developers can focus on the business aspects of their applications and no longer have to worry about availability, scalability, fault tolerance, over/underprovisioning, and other issues. In fact, serverless computing provides the cloud provider additional control over optimizing resources.

As cloud computing adoption becomes mainstream, the cloud services market offers vast profits. According to International Data Corporation (IDC), the worldwide public cloud services market grew 29.0% to a total revenue of USD 408.6 billion in 2021 [6]. Also, Gartner forecasts that the worldwide end-user spending on public cloud services will grow 20.4% to total USD 494.7 billion in 2022 and reach nearly USD 600 billion in 2023 [7]. Moreover, serverless computing with enormous economic growth potential is gaining popularity. Major cloud providers, including Amazon, Microsoft, Google, IBM, and others, have released serverless computing capabilities. As a result, investing in cloud computing is still promising and profitable.

To capitalize on the cloud, investors are interested in trading cloud stocks. In this paper, we loosely define cloud computing stocks (or cloud stocks) as IT companies that deliver cloud services over the internet and have shares traded in the financial market. The term refers to IT companies as a whole, not the specific cloud unit, as most of them do not spin off it. However, as is the case with high-growth stocks, investing in cloud stocks will have bumps on the road. The research problem of the paper is to study how a trading strategy will perform on cloud stocks, which are more volatile than others. The goal of the paper is to propose a trading strategy for cloud stocks. According to Treleaven, Galas, and Lalchand (2013), algorithmic trading is growing rapidly and is a fascinating research area. It refers to any form of trading using sophisticated algorithms to automate all or some part of the trade cycle. Inspired by their paper, we present an algorithmic trading strategy for cloud stocks.

This paper makes three contributions. First of all, it proposes an effective method, i.e., Simple Moving Average (SMA), for trading cloud stocks. It is the first paper to study a trading strategy for cloud stocks. We will develop more sophisticated algorithms based on this work in the future. Second, it adopts comprehensive statistical measures, including prediction errors, percentage errors, and goodness of fit, to systematically evaluate the approach. Third, it conducts extensive experiments on real market data over two decades and provides practical advice on how to set the parameters, i.e., the size of the sliding window and the length of time horizon.

The rest of the paper is organized as follows: Section 2 presents the techno-economic background. It first reviews the motivation and economics of cloud computing and serverless computing. Then, it examines the technical and economic aspects of financial technologies and algorithmic trading. Section 3 introduces algorithmic trading strategies. It first discusses common trading strategies. After that, it proposes an SMA approach for trading cloud stocks. Section 4 reports the experimental results. It first describes the experimental setup and evaluation metrics. Then, it reports experimental results and research findings. Section 4 concludes the paper. It first summarizes the research findings. After that, it mentions the limitations and discusses some future work.

2. Techno-Economic Background and Related Work

This section provides some background for cloud computing and financial technologies. Armbrust et al. (2010) argue that the key enabler of cloud computing is large data centers with hundreds or thousands of machines located at low-cost places. Because of economies of scale, cloud computing can reduce the cost of electricity, hardware, software, network bandwidth, and operations by a factor of five to seven, compared with traditional data centers. As a result, cloud computing can offer computing services below the cost of small- or medium-sized data centers yet still make a good profit. Cloud computing adopts the usage-based pricing model. It allows an organization to pay for computing resources by the hour and can lead to cost savings. Also, the absence of upfront capital expense in cloud computing allows for an enterprise to redirect capital to core business investments.

A newcomer—serverless computing—emerged with characteristics that are different from those of established cloud models [5]. It provides early adopters with further cost reductions, reduced operation effort, and scalability. The projected Compound Annual Growth Rate (CAGR) varies between 21% and 28% through 2028, and the projected market value is USD 36.8 billion by that time [8]. Serverless computing with enormous economic growth potential will drive cloud computing in the next decade [2]. However, serverless is a vague term in the ICT industry. It is used inaccurately to refer to less caring about servers. According to Castro, Ishakian, Muthusamy, and Slominski (2019), serverless computing is “a platform that hides server usage from developers and runs code on-demand automatically scaled and billed only for the time the code is running”. In other words, in serverless computing, developers do not need to worry about low-level details of server management and scaling and only pay for the execution time, not for idle servers, when processing requests or events.

As the focus is shifted from servers to applications, cloud computing enters its emerging second phase [9]. In the first phase, which is called serverful computing, system administration was simplified in managing computing infrastructure through virtualized servers. In the second phase, which is called serverless computing, cloud development is simplified by providing programming abstractions for developers through hiding servers. For example, programmers can define cloud functions and then specify how the functions should run. The second phase will change the way programmers work, just as the first phase changed how operators work. It should be noted that, in serverless computing, remote servers are still the invisible bedrock.

Financial technology (FinTech) is one of the disruptive innovations in IT and finance [10,11]. FinTech will reshape how the financial services industry structures and provisions. It has a transformative impact on financial sectors, including banking, insurance, investments, securities, etc. Globally, about 50% of financial consumers use at least one FinTech application. FinTech nurtures new business models, products, and services. FinTech aims to improve the efficiency of the financial services industry through modern IT. Artificial Intelligence (AI), machine learning, big data, cloud computing, blockchain, and cybersecurity, etc., play different roles in FinTech. Among them, AI, big data, and blockchain are considered three core technologies.

As one of the financial technologies, algorithmic trading (or algo trading for short) uses computer programs to make trading decisions [12]. Algo trading is widely used by investment banks and funds [13]. It is data-driven and involves learning, dynamic planning, reasoning, and decision-making. A trading process consists of five stages: data access and cleaning (financial, economic, news/social data), pre-trade analysis (data analysis), trading-signal generation (what and when to trade), trade execution (how to trade), and post-trade analysis (trade analysis). It should be noted that not all five stages are automated now. Computers are mainly used in the first two stages, while humans still supervise the last three stages. A recent survey on AI, machine learning (ML), and associated algorithms in capital markets can be found in Koshiyama, Firoozye, and Treleaven (2020) [14] where their computational strengths and weaknesses, as well as their impact on the capital markets, are discussed. As for trading strategies, momentum and reversal are well-known predictors of future market returns [15]. However, each has its pros and cons. This paper focuses on momentum as it deals with short-term prediction.

In view of its importance, top academic journals and conferences either dedicate special sections and tracks on FinTech or publish regular papers on it [16,17]. For example, leading experts in finance and information systems launched a call for papers on FinTech in a special section of Information Systems Research in 2017 [18]. Also, a top conference in computer science, International Joint Conference on Artificial Intelligence, published a special track on AI in FinTech in 2020 [19]. Still, leading academic institutions established new programs or units to train future FinTech professionals [20]. For instance, New York University initiated a FinTech specialization under its MBA programs in 2017. Queen’s University at Kingston launched Canada’s first Master’s program of Financial Innovation and Technology in 2020. As high-growth technology stocks, investing in cloud stocks is both rewarding and challenging. However, to the best of our knowledge, no research is devoted to studying a trading strategy for cloud stocks. As a result, this paper is motivated to fill this research gap.

3. Algorithmic Trading Strategies

This section discusses common trading strategies. Algorithmic trading strategies, which use computer algorithms to trade stocks, are beginning to receive attention from academia. Indeed, how to design algorithmic trading strategies has become a promising research topic in both IT and finance disciplines [21].

3.1. Momentum

A common trading strategy is momentum. It is “a trend following trading strategy that aims to capitalize on the continuance of existing trends in the market” [13]. Momentum relies on human common sense. It assumes that a large increase in the price of a stock will be followed by additional gains, while a large decrease will incur further losses. Momentum seems either optimistic or pessimistic and can generate profits in certain cases. However, momentum is moody and risky and could incur huge losses if it is not properly used. To implement momentum, first, an SMA can be used to capture upward and downward trends. It is an arithmetic moving average of stock prices over a time period. It is calculated by adding recent prices together and then dividing the sum by the number of trading days. Next, if the current price of a stock rises above the SMA, a buy signal is generated, and then the stock is bought. It is held until the price falls below the SMA, at which time a sell signal is triggered and the stock is sold.

3.2. Simple Moving Average

A Simple Moving Average (SMA) is a forecasting method that is appropriate for a time series with a horizontal pattern [22]. A horizontal pattern is present when the data fluctuate randomly around a constant mean over time. The SMA can adapt well to changes in a horizontal pattern. However, it is not appropriate, when considerable trends and other effects exist. The SMA is referred to as a smoothing method since its objective is to smooth out random fluctuations in the time series. Generally speaking, the SMA provides a high level of accuracy for short-term predictions, such as a forecast for the next time period. It uses the average of the most recent $k$ data values in the time series as the forecast for the next period. Formally, a moving average forecast of order $k$ is defined as follows.

$${\widehat{y}}_{t+1}={\displaystyle \frac{{{\displaystyle \sum }}_{i=t-k+1}^t{y}_i}{k}}$$

(1)

where ${\widehat{y}}_{t+1}$ is the forecast of the time series for Period $t+1$, $y_i$ the actual value of the time series in Period $i$, and $k$ the number of periods of time series data used to generate the forecast.

In fact, the goal of the paper is to use SMA to trade cloud stocks as the first step. According to the principle of Occam’s razor, the simplest explanation is usually the correct one and is often used in machine learning when choosing between different models. So, we rigorously test its performance. In the future, we will incorporate generative AI into this work.

3.3. Algorithmic Description

Algorithm 1 implements an SMA approach. It works as follows. First, in Line 1, the current price for Period $t$, $p_t$, is assigned with the last value $P\left[n-1\right]$ of stock price data. In Lines 2 and 3, the total price, $sum$, and the average price, $avg$, are initialized as 0. Next, the outer loop of Lines 4–14 calculates a moving average, for each Period $i$ from 0 to $n-k$. In Line 5, the starting of an interval, $j$ is updated with $i$. After that, the inner loop of Lines 6–8 calculates the sum of each Price $p_j$ in the interval from $P\left[j\right]$ to $P\left[j+k-1\right]$. Line 9 calculates the average of the $k$ prices. Last, in Lines 10–13, a BUY signal is generated if the current price, $p_t$ is greater than or equal to the average price, $avg$; otherwise, a SELL signal is generated.

Algorithm 1: SMA (P,n,k)

As to the running time of Algorithm 1, the inner loop repeats $k$ times, and the outer loop iterates $n-k+1$ times. As a result, the time complexity of Algorithm 1 is $O\left(k\right)\times O\left(n-k+1\right)=O\left(kn\right)$. In other words, its time complexity is linear, and so Algorithm 1 is efficient.

4. Evaluation and Analysis

This section describes the experiments and analyzes the results. To evaluate the SMA approach, we conduct extensive experiments on two representative cloud computing stocks. In the following, we detail the experimental setup, describe the evaluation metrics, and report the experimental results.

4.1. Experimental Setup

All experiments are conducted on a Dell XPS computer, with a 3.40 GHz Intel^® Core^TM i7-6700 CPU and a 32.0 GB RAM, running Microsoft Windows 10 OS. The experiments are implemented using Java under Oracle Netbeans IDE 12.2 with JDK 15.0.2. The dataset is the real market data obtained from Yahoo Finance (https://finance.yahoo.com, accessed on 30 June 2024). In the experiments, cloud stocks X (AMZN) and Y (MSFT) are chosen, and their daily close prices are used. Here, the criterion for selecting the two stocks is that they are major cloud providers. The rationale is that we focus on individual cloud stocks as the first step. In future, we will choose a Cloud Computing Index, such as Fidelity Cloud Computing ETF (FCLD), since it could better represent the industry.

As the two clouds were launched around 1999, the time period was chosen from 1 January 1999 to 31 December 2021, which spans over 23 years. This two-decade-long period witnessed two financial crises: the 2008 global financial crisis due to the subprime mortgage crisis and the 2020 stock market crash because of the COVID-19 pandemic. As the dataset contains dramatic market ups and downs, it suffices to stress-test the SMA approach. In fact, each year has about 252 trading days, and so the total number of data points is 5788 for cloud stocks X and Y.

4.2. Evaluation Metrics

To measure the accuracy of the SMA approach, we employ multiple evaluation metrics. It should be noted that no single metric is perfect, since each metric has its strengths and weaknesses. Here, the prediction error is defined as the difference between the actual value $y_i$ and the predicted value ${\widehat{y}}_i$ at time $i$.

$$e_i=y_i-{\widehat{y}}_i$$

(2)

The Mean Absolute Error (MAE) is one common metric used to measure accuracy. As its name suggests, MAE is the average of the absolute values of the prediction errors. It can avoid the problem of positive and negative prediction errors offsetting each other.

$$\mathrm{MAE}={\displaystyle \frac{1}{n}} {{\displaystyle \sum }}_{i=1}^n\left|y_i-{\widehat{y}}_i\right|$$

(3)

where $y_i$ is the actual value at Time $i$, ${\widehat{y}}_i$ the predicted value at Time $i$, and $n$ the number of time periods.

The Root Mean Squared Error (RMSE) is another common metric used to measure accuracy. RMSE is the rooted average of the squared prediction errors. It can avoid the problem of positive and negative errors offsetting one another, too.

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(4)

where $y_i$ is the actual value at Time $i$, ${\widehat{y}}_i$ the predicted value at Time $i$, and $n$ the number of time periods.

MAE and RMSE are quite useful metrics. However, it is not enough to use them alone on different datasets. In fact, the size of MAE and RMSE depends on the scale of the data. As a result, it cannot make comparisons for different time intervals or different time series. To make meaningful comparisons, we need relative or percentage error measures.

In the paper, for easy comparisons, we compute the ratio of the MAE to the mean of actual values to get the percentage error for MAE.

$${\delta }_{\mathrm{MAE}}={\displaystyle \frac{1}{\overline{y}}}\times \mathrm{MAE}\times 100$$

(5)

where $\overline{y}$ is the average of actual values. It is computed as

$$\overline{y}={\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n{y}_i$$

(6)

where $y_i$ is the actual value at Time $i$, and $n$ the number of time periods.

In a similar way, we compute the ratio of the RMSE to the mean of actual values to get the percentage error for RMSE.

$${\delta }_{\mathrm{RMSE}}={\displaystyle \frac{1}{\overline{y}}}\times \mathrm{MAE}\times 100$$

(7)

Generally speaking, a smaller value of MAE and RMSE means a more accurate forecast and is more desirable. Also, a smaller percentage error of MAE and RMSE is preferred. However, it should be noted that RMSE provides a relatively high weight to larger errors since the errors are squared before they are averaged. Therefore, RMSE is more useful than MAE in investments, where larger errors, which imply more volatility, are particularly undesirable.

4.3. Experimental Results on Cloud Stock X

In this section, we conduct experiments to evaluate the SMA approach using the metrics discussed above.

4.3.1. The Impact of Sliding Window

Here, the impact of the sliding window $k$ for SMA is studied. It is generally assumed that a short sliding window will produce a more accurate prediction since it is more responsive to the market. To test whether this assumption is true or not, we first formulate it as a research hypothesis.

Hypothesis 1A (H1A). 

All else being equal, the longer the sliding window k, the larger the prediction error and the less favorable the performance of SMA.

Hypothesis 1B (H1B). 

All else being equal, the longer the sliding window k, the larger the percentage error and the less favorable the performance of SMA.

To test whether H1A and H1B hold or not, we conduct experiments on cloud stock X using the daily close price data of the year 2021. The dataset used to test the parameter and derive the model is called the training set. As to the training data, there are 252 trading days in 2021. The first trading day is 4 January 2021, and the last trading day is 31 December 2021. In the experiments, we vary Parameter $k$ from 10 days to 240 days, with a step of 10 days.

Table 1. Prediction errors of SMA on cloud stock X in 2021 ($k=10\text{–}240$).

	10 Days	20 Days	30 Days	40 Days	50 Days	60 Days	70 Days	80 Days
MAE	3.27/1.96%	4.94/2.96%	5.94/3.57%	5.83/3.51%	5.71/3.44%	5.73/3.45%	5.77/3.48%	6.25/3.78%
RMSE	4.17/2.50%	5.99/3.59%	7.04/4.23%	7.06/4.26%	7.04/4.25%	7.04/4.25%	7.13/4.30%	7.72/4.66%
	90 Days	100 Days	110 Days	120 Days	130 Days	140 Days	150 Days	160 Days
MAE	6.54/3.96%	6.57/3.98%	6.89/4.18%	6.25/3.81%	5.31/3.27%	5.25/3.26%	5.71/3.54%	5.94/3.69%
RMSE	8.23/4.99%	8.49/5.14%	8.76/5.31%	8.02/4.90%	6.46/3.98%	6.55/4.06%	7.14/4.43%	7.39/4.59%
	170 Days	180 Days	190 Days	200 Days	210 Days	220 Days	230 Days	240 Days
MAE	6.32/3.93%	6.85/4.29%	7.55/4.76%	6.90/4.33%	5.78/3.60%	4.26/2.63%	5.79/3.59%	8.55/5.39%
RMSE	7.77/4.83%	8.40/5.26%	9.03/5.69%	8.54/5.36%	7.45/4.64%	5.58/3.44%	6.97/4.32%	9.05/5.71%

shows the prediction errors and percentage errors of SMA on cloud stock X in 2021. Here is how to read the table. For each sliding window, we compute the MAE and RMSE and their relative values. As an example, for the sliding window of 10 days, the MAE is 3.27 and its relative value is 1.96% (i.e., “3.27/1.96%”); MAE and its relative value are calculated by Equations (3) and (5), respectively. The RMSE is 4.17 and its relative value is 2.50% (“4.17/2.50%”). RMSE and its relative value are calculated by Equations (4) and (7), respectively.

From Table 1, we can draw two observations. First, as the sliding window increases, the prediction errors and percentage errors of both MAE and RMSE increase, with some fluctuations. It follows that Hypothesis 1A and Hypothesis 1B generally hold true in our experiments. The practical and managerial implication of this finding is to choose a small and appropriate sliding window, if one desires a more accurate model. However, it should be noted that it is difficult, if not impossible, to find the best sliding window. In fact, the right sliding window could only be found by try and error. For this reason, in the paper, we will set the sliding window as 10 when appropriate.

Second, for the same sliding window, the prediction errors and percentage errors of RMSE are consistently larger than that of MAE. As mentioned in Section 4.2, RMSE assigns a higher weight to larger errors. As a result, RMSE will be more affected by the extreme values than MAE in the presence of outliers.

In contrast, MAE provides an equal weight for all errors, and so it will not be more affected by outlying values. For this reason, it is not surprising that on the same dataset, the prediction errors and percentage errors of RMSE are always larger than those of MAE. In other words, if a model generates large forecast errors, it will be penalized more by RMSE than MAE. In this sense, RMSE is more capable of identifying such a model than MAE. The practical and managerial implication of this finding is to choose RMSE over MAE in making investment decisions as this paper intends to do, if one desires a less volatile model.

Figure 1 plots the prediction errors of SMA on cloud stock X in 2021. Here is how to read the figure. The horizontal axis is the sliding window where each unit represents 10 days. The vertical axis denotes the prediction error. From the figure, we can draw two observations. First, the blue line, which stands for MAE, is always below or less than the dashed red line, which stands for RMSE, for the reason mentioned above. Second, the pattern of the blue line near-perfectly matches that of the red line. It implies that MAE can capture the essence of SMA, just as RMSE does.

Figure 2 plots the percentage errors of SMA on cloud stock X in 2021. Here is how to read the figure. The horizontal axis is again the sliding window, where each unit represents 10 days. The vertical axis denotes the percentage error. From the figure, we can draw two observations. First, the blue line, which stands for percentage errors of MAE, is again below or less than the dashed red line, which stands for percentage errors of RMSE. Second, the pattern of the blue line almost agrees with that of the red line. In particular, for both MAE and RMSE, the pattern of percentage errors is like that of prediction errors, even the two types of errors are of different magnitude.

4.3.2. The Impact of Time Horizon

Here, the impact of the time horizon $h$ for the SMA approach is studied. The conventional wisdom is that a longer time horizon is associated with lower volatility. However, this proposition is debatable in the financial literature. To test whether it is less volatile over a longer time horizon, we again formulate it as a research hypothesis.

Hypothesis 2A (H2A): 

All else being equal, the longer the time horizon h, the smaller the prediction error and the more desirable the performance of SMA.

Hypothesis 2B (H2B): 

All else being equal, the longer the time horizon h, the smaller the percentage error and the more desirable the performance of SMA.

To test whether H2A and H2B hold or not, we conduct experiments on cloud stock X, using the daily close price data of the years from 1999 to 2021. As to the training data, there are 23 trading years in total. The first trading day is 4 January 1999, and the last trading day is 31 December 2021. In the experiments, we vary Parameter $h$ from 1 year to 23 years, with a step of 1 year.

Table 2. Prediction errors of SMA on cloud stock X ($h=1\text{–}23$).

	1 Year	2 Years	3 Years	4 Years	5 Years	6 Years	7 Years	8 Years
MAE	0.26/7.75%	0.22/7.53%	0.17/7.73%	0.14/7.45%	0.12/6.71%	0.12/6.15%	0.11/5.67%	0.10/5.37%
RMSE	0.34/10.02%	0.29/9.99%	0.24/11.26%	0.21/11.66%	0.19/10.65%	0.18/9.69%	0.17/9.05%	0.16/8.64%
	9 Years	10 Years	11 Years	12 Years	13 Years	14 Years	15 Years	16 Years
MAE	0.10/5.03%	0.11/4.95%	0.11/4.73%	0.12/4.30%	0.13/4.02%	0.14/3.66%	0.15/3.32%	0.17/3.16%
RMSE	0.16/8.00%	0.17/7.61%	0.17/7.25%	0.18/6.47%	0.20/6.16%	0.22/5.61%	0.23/5.09%	0.26/4.92%
	17 Years	18 Years	19 Years	20 Years	21 Years	22 Years	23 Years
MAE	0.19/2.99%	0.22/2.79%	0.25/2.51%	0.34/2.52%	0.41/2.37%	0.56/2.48%	0.68/2.35%
RMSE	0.32/5.00%	0.39/4.92%	0.46/4.53%	0.76/5.54%	0.89/5.17%	1.35/5.99%	1.58/5.48%

shows the prediction errors and percentage errors of SMA on cloud stock X from 1999 to 2021, where the sliding window is set as 1 year. Here is how to read the table. The time horizons are set as follows. The 1-year time horizon is the year 1999. The 2-year time horizon is from the year 1999 to 2000. The 3-year time horizon is from the year 1999 to 2001 and so on and so forth. For each time horizon, we compute the MAE and RMSE and their relative values.

From Table 2, we can draw two observations. First, as the time horizon increases, the prediction errors of both MAE and RMSE generally increase. It follows that Hypothesis 2A holds false in our experiments. However, the percentage errors of both MAE and RMSE generally decrease. It follows that Hypothesis 2B holds true in our experiments. The practical and managerial implication of this finding is to choose a reasonable time horizon so that both the prediction errors and the percentage errors are at an acceptable level. Second, for the same time horizon, the prediction errors and percentage errors of RMSE are consistently larger than those of MAE for the above-mentioned reason.

Figure 3 plots the prediction errors of SMA on cloud stock X from 1999 to 2021. Here is how to read the figure. The horizontal axis is the time horizon, and there are 23 time horizons in total. The vertical axis denotes the prediction error. From the figure, we can draw two observations. First, the blue line, which stands for MAE, is again below or less than the dashed red line, which stands for RMSE. Second, the two lines start to go down slightly from 1999 (Time Horizon 1) to 2008 (Time Horizon 10), then go up steadily from 2008 to 2016 (Time Horizon 18), and then go up considerably from 2016 to 2021 (Time Horizon 23). In fact, the price of cloud stock X shows a similar trend, as reflected in the prediction errors. It slows down somewhat from 1999 to 2008, improves steadily after the 2008 financial crisis until 2016, and speeds up significantly in the recent 5 years.

Figure 4 plots the percentage errors of SMA on cloud stock X from 1999 to 2021. Here is how to read the figure. The horizontal axis is again the time horizon, and there are 23 time horizons in total. The vertical axis denotes the percentage error. From the figure, we can draw two observations. First, the blue line, which stands for percentage errors of MAE, is again below or less than the dashed red line, which stands for percentage errors of RMSE. Second, the two lines start to go up from 1999 (Time Horizon 1) to 2001 (Time Horizon 3), and then go down continuously from 2002 (Time Horizon 4) to 2021 (Time Horizon 23), with some fluctuations in the recent 5 years. In fact, the pattern of percentage errors is the opposite of that of the prediction errors. It shows that the relative percentage errors of MAE and RMSE decrease constantly over a longer time horizon, even though the absolute prediction errors increase somewhat.

4.3.3. Evaluating the Accuracy of SMA

Here, we assess the accuracy of the SMA approach on the test set. It is important to estimate its accuracy before we deploy it in the real environment. The dataset used to estimate the accuracy of the model is called a test set. In the following, we will use the daily close price data of cloud stock X from the first half of 2022 to evaluate the accuracy of SMA, where the sliding window is set as 10 days and the time horizon is a half year. As to the test data, there are 124 trading days. The first trading day is 3 January 2022, and the last trading day is 30 June 2022.

To rigorously evaluate SMA, we introduce another metric, i.e., R-squared. R-squared ($R^2$), also called the coefficient of determination, measures how well a statistical model predicts an outcome. $R^2$ measures the amount of variation that can be explained by the model; that is, the percentage of correct predictions returned by the model.

$$R^2=1-{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{(y_i-\overline{y})}^2}}$$

(8)

where $y_i$ is the actual value at Time $i$, ${\widehat{y}}_i$ the predicted value at Time $i$, $\overline{y}$ is the average of actual values, and $n$ the number of time periods.

Unlike the correlation explaining the strength of the relationship between a dependent variable and an independent variable, R-squared measures the extent the variance of one variable explaining that of the other variable. R-squared values range from 0 to 1 and are represented as percentages from 0% to 100%. For example, if the $R^2$ of a model is 0.70, then about 70% of the observed variance can be explained by the model. In other words, we can interpret that 70% of the model’s predictions are correct, and the variation of the errors is 30%.

Table 3. Performance of SMA on cloud stock X in 2022 ($k=10, h=0.5$).

Metrics	Value
MAE	6.69/4.71%
RMSE	8.30/5.84%
R-squared	83.25%

shows the prediction errors and percentage errors of SMA on cloud stock X in the first half of 2022. From Table 3, we can draw three conclusions. First, the SMA is a quite accurate model. As can be seen in the table, the prediction error of MAE is 6.69, and its percentage error is 4.71%. The prediction error of RMSE is 8.30, and its percentage error is 5.84%. Both the prediction errors and percentage errors of MAE and RMSE are moderate, even the stock market suffered a huge loss in the first half of 2022 because of the COVID-19 disruption, the high inflation, the Ukraine–Russia conflict, etc.

Second, the prediction errors and percentage errors of RMSE are greater than that of MAE. It confirms that RMSE is more effective than MAE to capture market fluctuations. Third, the value of R-squared shows that 83.25% of the variance can be explained by SMA, which indicates a good model. R-squared is calculated by Equation (8).

4.4. Experimental Results on Cloud Stock Y

In this section, we conduct another experiment to evaluate the SMA approach on cloud stock Y.

4.4.1. The Impact of Sliding Window

To test whether H1A and H1B hold or not, we conducted experiments on cloud stock Y using the daily close price data of the year 2021. As to the training data, there are 252 trading days in 2021. The first trading day is 4 January 2021, and the last trading day is 31 December 2021. In the experiments, we varied Parameter $k$ from 10 days to 240 days, with a step of 10 days.

Table 4. Prediction errors of SMA on cloud stock Y in 2021 ($k=10\text{–}240$).

	10 Days	20 Days	30 Days	40 Days	50 Days	60 Days	70 Days	80 Days
MAE	4.72/1.72%	7.97/2.94%	10.04/3.74%	10.26/3.87%	10.53/4.01%	11.96/4.60%	13.67/5.29%	14.74/5.75%
RMSE	5.89/2.15%	9.61/3.54%	12.26/4.57%	12.57/4.73%	12.75/4.86%	14.38/5.52%	16.36/6.32%	17.72/6.91%
	90 Days	100 Days	110 Days	120 Days	130 Days	140 Days	150 Days	160 Days
MAE	14.83/5.85%	14.48/5.77%	13.90/5.60%	12.68/5.16%	11.14/4.58%	10.94/4.54%	12.60/5.25%	15.18/6.35%
RMSE	17.84/7.03%	17.42/6.94%	16.90/6.80%	15.63/6.36%	13.75/5.66%	13.93/5.78%	15.89/6.62%	18.45/7.71%
	170 Days	180 Days	190 Days	200 Days	210 Days	220 Days	230 Days	240 Days
MAE	18.24/7.66%	22.40/9.51%	27.21/11.71%	29.86/12.89%	32.87/14.23%	36.38/15.77%	44.95/19.95%	55.46/25.51%
RMSE	21.63/9.08%	25.18/10.69%	28.75/12.37%	31.37/13.55%	34.52/14.94%	38.27/16.58%	46.07/20.45%	55.59/25.57%

shows the prediction errors and percentage errors of SMA on cloud stock Y in 2021.

From Table 4, we can confirm two observations identified on cloud stock Y. First, as the sliding window increases, the prediction errors and percentage errors of both MAE and RMSE increase. It shows that Hypothesis 1A and Hypothesis 1B hold true on cloud stock Y, too. In the following, we will set the sliding window as 10. Second, for the same sliding window, the prediction errors and percentage errors of RMSE are larger than that of MAE on cloud stock Y, too.

Figure 5 plots the prediction errors of SMA on cloud stock Y in 2021. From the figure, we can confirm two observations identified on cloud stock X. First, the blue line, which stands for MAE, is always below or less than the dashed red line, which stands for RMSE. Second, the pattern of the blue line near-perfectly matches that of the red line, too.

Figure 6 plots the percentage errors of SMA on cloud stock Y in 2021. From the figure, we can confirm two observations identified on cloud stock X. First, the blue line, which stands for percentage errors of MAE, is below or less than the dashed red line, which stands for percentage errors of RMSE. Second, the pattern of the blue line almost agrees with that of the red line, too.

4.4.2. The Impact of Time Horizon

To test whether H2A and H2B hold or not, we conduct experiments on cloud stock Y, using the daily close price data of the years from 1999 to 2021. As to the training data, there are 23 trading years in total. The first trading day is 4 January 1999, and the last trading day is 31 December 2021. In the experiments, we vary Parameter $h$ from 1 year to 23 years, with a step of 1 year.

Table 5. Prediction errors of SMA on cloud stock Y ($h=1\text{–}23$).

	1 Year	2 Years	3 Years	4 Years	5 Years	6 Years	7 Years	8 Years
MAE	1.33/3.09%	1.55/3.75%	1.41/3.73%	1.25/3.56%	1.12/3.35%	0.99/3.08%	0.90/2.86%	0.84/2.72%
RMSE	1.75/4.05%	2.06/5.00%	1.88/4.96%	1.69/4.82%	1.55/4.65%	1.43/4.43%	1.33/4.25%	1.26/4.11%
	9 Years	10 Years	11 Years	12 Years	13 Years	14 Years	15 Years	16 Years
MAE	0.80/2.62%	0.80/2.63%	0.78/2.62%	0.76/2.58%	0.74/2.52%	0.72/2.46%	0.71/2.41%	0.70/2.33%
RMSE	1.22/3.98%	1.20/3.95%	1.16/3.92%	1.13/3.84%	1.10/3.77%	1.07/3.67%	1.06/3.59%	1.04/3.45%
	17 Years	18 Years	19 Years	20 Years	21 Years	22 Years	23 Years
MAE	0.72/2.30%	0.73/2.23%	0.73/2.12%	0.78/2.05%	0.83/1.97%	1.01/2.06%	1.17/2.00%
RMSE	1.06/3.42%	1.07/3.30%	1.07/3.11%	1.15/3.04%	1.24/2.93%	1.79/3.66%	2.14/3.65%

shows the prediction errors and percentage errors of SMA on cloud stock Y from 1999 to 2021, where the sliding window is set as 1 year. The time horizon is set the same as cloud stock X. That is, the 1-year time horizon is the year 1999. The 2-year time horizon is from the year 1999 to 2000. The 3-year time horizon is from the year 1999 to 2001 and so on and so forth.

From Table 5, we can draw two observations. First, as the time horizon increases, the prediction errors of both MAE and RMSE first increase, then decrease, and then again increase. Overall, the prediction errors of MAE slightly decrease, and that of RMSE slightly increases. It roughly confirms that Hypothesis 2A holds false in our experiments. However, the percentage errors of both MAE and RMSE generally decrease. It confirms that Hypothesis 2B holds true in our experiments. Second, for the same time horizon, the prediction errors and percentage errors of RMSE are consistently larger than that of MAE.

Figure 7 plots the prediction errors of SMA on cloud stock Y from 1999 to 2021. From the figure, we can draw two observations. First, the blue line, which stands for MAE, is again below or less than the dashed red line, which stands for RMSE. Second, the two lines start to go up from 1999 (Time Horizon 1) to 2000 (Time Horizon 2), then go down continually from 2000 to 2014 (Time Horizon 16), and then again go up significantly from 2014 to 2021 (Time Horizon 23). In fact, the price of cloud stock Y shows a similar trend, as reflected in the prediction errors. It goes up from 1999 to 2000, then drops continually until 2014, and then again goes up significantly in the recent 7 years.

Figure 8 plots the percentage errors of SMA on cloud stock Y from 1999 to 2021. From the figure, we can confirm two observations. First, the blue line, which stands for percentage errors of MAE, is below or less than the dashed red line, which stands for percentage errors of RMSE. Second, the two lines start to go up from 1999 (Time Horizon 1) to 2000 (Time Horizon 2), then go down continuously from 2000 to 2019 (Time Horizon 21), and then again go up from 2019 to 2021 (Time Horizon 23). It confirms that the relative percentage errors of MAE and RMSE decrease over a longer time horizon; even the absolute prediction errors increase. In addition, Figure 3 and Figure 7 have different trends, but Figure 4 and Figure 8 have similar trends. The reason could be that the errors in Figure 3 and Figure 7 are measured in absolute values, while the errors in Figure 4 and Figure 8 are measured in relative values.

4.4.3. Evaluating the Accuracy of SMA

Here, we assess the accuracy of the SMA approach on the test set. In the following, we will use the daily close price data of cloud stock Y from the first half of 2022 to evaluate the accuracy of SMA, where the sliding window is set as 10 days and the time horizon is a half year. As to the test data, there are 124 trading days. The first trading day is 3 January 2022, and the last trading day is 30 June 2022.

Table 6. Performance of SMA on cloud stock Y in 2022 ($k=10, h=0.5$).

Metrics	Value
MAE	7.87/2.73%
RMSE	9.41/3.26%
R-squared	76.96%

shows the prediction errors and percentage errors of SMA on cloud stock Y in the first half of 2022. From Table 4, we can confirm three conclusions. First, the SMA is an accurate model. As can be seen in the table, the prediction error of MAE is 7.87, and its percentage error is 2.73%. The prediction error of RMSE is 9.41, and its percentage error is 3.26%. The prediction errors of MAE and RMSE are greater than those of cloud stock X, but the percentage errors are less than those of cloud stock X.

Second, the prediction errors and percentage errors of RMSE are greater than those of MAE. It confirms again that RMSE is more effective than MAE to capture the market fluctuations. Third, the value of R-squared is 76.96% and is less than that of cloud stock X, which indicates a reasonably good model.

4.5. Discussion of Findings

There are several important findings from this study. A notable result is that SMA is an effective model. The experiments on stocks X and Y show that the percentage errors of both MAE and RMSE are quite low, approximately 3% to 6%. Another salient finding is that RMSE is a valid and effective measure. The two experiments demonstrate that both the prediction errors and percentage errors of RMSE are greater than that of MAE. The implication for investors is to choose RMSE over MAE. The third finding is that SMA is a model of goodness of fit. The experiments illustrate that the value of R-squared is around 80%.

Regarding the parameters, there are another two findings. First, the longer the sliding window, the less favorable the SMA. The experiments show that the longer the sliding window, the larger the prediction error and percentage error. In fact, Hypothesis 1A and Hypothesis 1B hold true in the experiments. The implication for investors is to choose a reasonably small sliding window. Second, the longer the time horizon, the more desirable the SMA. The experiments show that the longer the time horizon, the smaller the percentage error, but the larger the prediction error. In fact, Hypothesis 2B holds true, but Hypothesis 2A holds false in the experiments. The implication for investors is to choose a reasonably long time horizon.

In summary, the SMA is an effective approach. If its parameters are properly set, it can achieve satisfying performance for cloud investors. So, this study fills the research gap by proposing a trading strategy for cloud stocks. However, it should be noted that the financial market is hard, if not impossible, to predict. A model that performs good in the past might not do well in the future. For this reason, the SMA method should be used with caution. In the future, we will enhance it with generative AI.

5. Conclusions and Future Work

This section summarizes the paper and discusses some future work. After a decade of rapid growth, cloud computing has become the backbone of modern IT infrastructure. Once considered a hyped term, cloud computing is everywhere today. It has been used in many types of applications, including email services, photo storing sites, online backup, file transfer applications, etc. As cloud computing adoption becomes mainstream, the cloud services market offers vast profits. Also, serverless computing with enormous economic growth potential is becoming popular and will drive cloud computing in the next decade. As a result, investing in cloud computing is still promising and profitable.

As is the case with high-growth stocks, investing in cloud stocks will have bumps on the road. It is not clear how a trading strategy will perform on cloud stocks. So, this paper proposes an SMA approach to trade cloud stocks. To evaluate its effectiveness, we conduct extensive experiments on two cloud stocks with real market data. Results show that SMA can achieve satisfying performance, in terms of prediction errors and goodness of fit. In addition, we provide practical advice on how to set the parameters and choose the metrics. First, a small and appropriate sliding window is preferred if one desires a more accurate model. Second, a reasonable time horizon is chosen to keep the prediction errors and the percentage errors at an acceptable level. Third, RMSE is preferred if one desires a less volatile model.

However, it should be noted that this study has three limitations. First, the two stocks used in the experiments are not pure cloud stocks. In fact, the companies that issue the two stocks involve cloud computing and other businesses. It is difficult, if not impossible, to determine how much cloud computing contributes to their stock price. It could be improved by choosing a Cloud Computing ETF, which has a broader range of cloud stocks. Second, the time horizon of the test set is quite short. In fact, the test set only contains daily close price data of the two stocks from the first half of 2022. As a result, we conjecture that it could negatively impact the performance of SMA. It could be improved by extending the evaluation period to a longer time horizon. Third, as a technical indicator, SMA relies on historical data, and so it tends to lag the market. It could be enhanced by integrating with sentiment analysis through analyzing news information. In the future, first, we will enhance SMA by incorporating generative AI and compare it with other trading strategies. More specifically, we will leverage Large Language Models (LLMs) to conduct sentiment analysis on news information, which is quite effective in our preliminary research, and integrate it with technical analysis to enhance SMA. Second, we will consider statistical significance tests and the effect sizes. Third, we will try to tune the parameters when possible. Fourth, we will consider coding trading rules and risk management as well. In addition, we will consider sensitivity analysis to determine the effect that changes in market conditions have on the approach.

In conclusion, cloud computing and serverless computing in particular will continue to grow and remain as investment opportunities for technology investors. Financial technologies and algorithmic trading in particular will play an important role in investment decision-making. SMA is an effective approach for trading cloud stocks. It performs quite well in terms of MAE, RMSE, and R-squared. In the future, we will enhance SMA with generative AI and use it to trade emerging technology stocks.