Next Article in Journal
Optimizing Time Series Models for Water Demand Forecasting
Previous Article in Journal
Applying Pump Affinity Laws to an Isolated Solar-Powered Pumping Station
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Engineering Proceedings
Volume 68
Issue 1
10.3390/engproc2024068062
engproc-logo
Submit to this Journal
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Proceeding Paper

Decomposing the Sri Lanka Yield Curve Using Principal Component Analysis to Examine the Term Structure of the Interest Rate †

by
K P N Sanjeewa Dayarathne
* and
Uthayasanker Thayasivam
*
Department of Computer Science & Engineering, University of Moratuwa, Moratuwa 10400, Sri Lanka
*
Authors to whom correspondence should be addressed.
†
Presented at the 10th International Conference on Time Series and Forecasting, Gran Canaria, Spain, 15–17 July 2024.
Eng. Proc. 2024, 68(1), 62; https://doi.org/10.3390/engproc2024068062
Published: 27 August 2024
(This article belongs to the Proceedings of The 10th International Conference on Time Series and Forecasting)
Browse Figures
Versions Notes

Abstract

:
In this study, we delve into the dynamics of the Sri Lankan government bond market, building upon prior research that focused on the application of principal component analysis (PCA) in modelling sovereign yield curves. Our analysis encompasses data spanning from January 2010 to August 2022. The study applied several PCA variants such as multivariate PCA, Randomized PCA, Incremental PCA, Sparse PCA, Functional PCA, and Kernel PCA on smoothed data. Kernel PCA was found to explain the majority of the variation associated with the data. Findings reveal that the first principal component accounted for a substantial 97.69% of the variations in yield curve movements, 2nd PCA accounted for 1.88%, and 3rd for 0.42%. These results align with previous research, which generally posits that the initial three principal components tend to elucidate around 95% of the fluctuations within the term structure of yields. Our results question the empirical findings, which state that the 1st PCA represents the longer tenor of the yield curve. In Sri Lanka, instead, the 1st PCA represents the 3-year bond yields. It may be because of the liquidity constraints in underdeveloped frontier markets, where longer tenor yields do not react fast enough to reflect the movement of the yield curve. The 2nd PCA represents the slope of the yield curve which is the yield difference of a 10-year T-Bond and 3 months T-Bill. The 3rd PCA which represents the curvature of the yield curve attributed to 2 × 3 years T-Bond yield—3 months T-bill10-year T-Bond.

1. Introduction

Yield curve prediction was an enthusiastic topic among capital market researchers [1] for a long time, but data science (Puglia & Tucker, 2020) [2] techniques have reshaped these efforts to an elevated status. Understanding the underlying structure of the term interest [3] rate or examining the functional behavior of the yield curve is a long outstanding question that many scholars are searching for. Due to the complexity of the yield curve behavior in different economies (developed, frontier, underdeveloped) understanding and identifying the structure with fewer components has been a challenge.
The traditional regression method was not sufficient enough to decompose the yield curve and understand its functional behavior [4]. The Nelson–Siegel model, introduced in 1987, holds a prominent place in the realm of yield curve fitting. Nelson–Siegel’s model utilizes exponential functions to model the smooth, non-linear characteristics of yield curves accurately. This approach or the proposed structure has been landmarked in the domain of modelling the yield curve. The change of the parameter over time or in other words the dynamic nature of the Nelson–Siegel model parameters allowed it to generate higher accuracy in this exercise. Decomposed underlined factors are associated with economic factors and represented by different forms of interest rates as well [5]. Since the maturity level of the respective capital markets would vary from developed to underdeveloped, the representation of the associated factors could also vary from the level of development. Hence the parameters of the Nelson–Siegel model should not be blindly applied, and it is required to be examined.
Their functional form suggested the applicability of the Principal Component Analysis (PCA) for yield curve modelling. PCA has been used for the dimension reduction technique for many years and has provided one way to resolve the above matter as it allows identification of the structure of the yield curve along with a few components. Principal components offer a highly intuitive interpretation by representing the most distinctive yield curve perturbations.
In this paper, the different variants of the PCA method have been used in describing the dynamics of the Sri Lanka Government Securities yield curve. The data for the period of 2010 to 2022 was used for the experiment. Studies have uncovered that the initial three principal components can be understood as representing the yield curve’s level, slope, and curvature, typically accounting for approximately 90% to 95% of the variations in yields [6,7,8], especially in the developed capital markets.
Out of several variants of PCA approaches, Kernal PCA [9] was found to be the best to uncover the structure. As the first principal component explained 97.69% of the yield curve changes, the second component explained 1.88%, and the third component explained 0.42%. This study questioned the traditional proxies identified for the 1st and 2nd principal component for countries like Sri Lanka, which is frontier markets. Contradicting the previous proxy for 1st principal component, which is the 10-year Bond rate (developed capital markets), the study proposed a 3-year bond rate for the Sri Lanka capital market. Further, the traditional proxy for the 2nd principal component is the yield difference between the longest tenor and medium tenor. However, the study proposed yield differences between the longest tenor and shortest tenor.
In studies carried out in developed capital markets such as the USA, EU, and Canada, the percentage of variation explained by each principal component seems to be substantially different. Since each principal component acts as a proxy for economic variables, the finding is valuable for policymakers in the government and private treasury traders in various financial institutions. It further highlights the importance of the monetary policies that are adopted concerning the economic behavior of the country, as the structure of the yield curve is different from developed countries to underdeveloped frontier markets like Sri Lanka.
The rest of the sections of this paper illustrate the background of the formation of the yield curve, the approach of the principal component on the data structures, the methodology to examine different variants of the PCA and data structure, and finally the experiment and discussion.

2. Literature Review

This section covers the panel data approach of the yield curve followed by the functional form of the yield curve. Then, it discusses the theoretical foundation for the yield curve to view as functional data. It is followed by the functional approach of the Nelson–Siegel model. The role of PCA in discovering the functional structure is discussed subsequently. Randomized PCA, Incremental PCA, Non-linear PCA, Sparse PCA, and Functional PCA along with Kernal PCA for functional data are discussed as a separate section under the Literature Review. The Nelson–Siegel model is the most adopted model to understand the yield curve, followed by the Nelson–Siegel Svensson Model [10]; however, recent studies by Valcu and Wickens (2012) [11], as well as [12], have uncovered vulnerabilities in traditional parsimonious yield curve models, such as the Nelson–Siegel model, particularly in their sensitivity to outliers and extreme values.

2.1. Panel Data Approach for the Yield Curve

On the path of modeling the yield curve, understanding the data structure is very important. Traditional panel data comprises repeated observations of the same set of cross-sectional units over time. These units can encompass individuals, firms, schools, cities, or any grouping of entities that can be tracked longitudinally [13].
Wooldridge in his book “Econometric Analysis of Cross Section and Panel Data” states how panel data analysis methods can be applied to financial data, including yield curve data, to gain deeper insights into economic relationships. The authors of [14] also discuss the yield curve and use panel data analysis to explore the predictive power of the yield curve in forecasting economic recessions, demonstrating how panel data methods can be applied to yield curve data.
Yield curve data can indeed be considered as a form of panel data, as they involve multiple observations over time for a range of financial instruments. Let us probe deeper into this concept with some explanations. Multiple Time Observations: Panel data, as mentioned earlier, encompass both a cross-sectional dimension (different financial instruments) and a time series dimension (observations at different points in time). In the context of yield curve data, the cross-sectional dimension comprises various bond maturities or tenors, while the time series dimension involves interest rate observations at different points in time. Yield curve data capture how interest rates change over time, reflecting the dynamic nature of financial markets. As market conditions, economic factors, and central bank policies evolve, yield curves exhibit variations, providing insight into intra-individual dynamics. Using yield curve data as panel data allow for a more robust and comprehensive analysis. Researchers can employ econometric techniques designed for panel data analysis to better understand the relationships between different parts of the yield curve, forecast future interest rates, and assess the impact of economic events and policies. The yield curve occupies a three-dimensional data structure. Under the concept of yield curve data, two dimensions are associated with time, which is calendar time and tenor (remaining maturities) of the financial instrument (Bond) e.g., 1 year, 2 years, 5 years, etc. Therefore, the yield curve data are a specialized branch of the panel data.
The yield curve dataset can be viewed as the traditional panel data approach as well (Table 1), where the calendar date and the tenor of the security are two dimensions, and the yield is the other dimension. Even though the yield curve can be viewed as traditional panel data, it accounted for more information than the traditional panel dataset. That is, their two axes are related to the sequence order of time. i.e., calander date and tenor. The traditional panel data accounted for only one factor with the sequence order of time. This is unique to the yield curve data.
Furthermore, interestingly, each panel has a similar kind of structure. It means each panel of the data (refer to Table 2) behave in a similar way, which is not common for all the panel data either. But there are similar kinds of data such as the temperature of the month of the year across the cities, and child growth patterns [15], and heart rate data over time from individuals undergoing stress tests. This data represents heart rate as a function of time during the test [16] and, the growth curve for one infant during the first 40 days from birth [17], as well as knee and hip angles for one boy during his gait cycle [18]. Ref. [19] examined the structure of populations of complex objects, such as images as repeated functions, and [20,21] examined the climatic variation. Ramsay in 2000 examined the handwritten style as panel data as it repeats several times. This underlined structure (pattern) can be modeled as a curve or function; the method that is used to explore this data has been identified as the function data analysis. Hence, the yield curve analysis can be carried out as functional data analysis.

2.2. Theoretical Foundation for the Functional Form of the Yield Curve Data

This functional form is entirely not because of the arbitrary incidents, but because of the fundamental economic and risk theories. The Pure expectation Theory, Market Segmentation Hypothesis, and Liquidity Premium Theory broadly develop this theoretical foundation for the functional presentation of the yield curve [22].
The upward-sloping yield curve is the most prevalent type, characterized by lower interest rates on short-term securities compared to long-term ones. According to the expectation theory, bond investors are generally indifferent to the maturity of bonds when making investment choices [23]. They will only hold a bond if its expected return exceeds that of another bond with a different maturity. Conversely, this theory implies that the yields on long-term bonds will average out to be equal to the average of short-term bonds, allowing for perfect substitution between bonds of different maturities. Consequently, an investor’s return over a two-year investment horizon is the same whether they initially invest in a one-year bond and then, upon maturity, reinvest in another one-year bond or if they invest directly in a two-year bond. This suggests that an increase in current interest rates tends to lead to higher future rates, as long-term rates are influenced by the average of short-term rates. However, while the pure expectations theory provides insights into the behavior of the yield curve’s term structure, it falls short of explaining the specific upward slope observed in many cases.
Another significant theory in the realm of bond markets is the market segmentation theory. This theory posits that the demand for securities with varying maturities hinges on investors’ perceptions and preferences, leading to a segmentation of demand along the yield curve [24]. Consequently, securities with differing maturities are not perfect substitutes since distinct investors exhibit varying preferences for one security over another. As a result, the yield curve exhibits different patterns based on the interplay of supply and demand. Furthermore, it underscores that economic factors, such as inflation, may have a stronger correlation with bonds having longer maturities, while factors like excess liquidity may exert an influence on bonds with shorter maturities. In essence, the expected returns from a bond of one maturity does not impact the demand for a bond with a different maturity date. This theory forms the foundation for yield curve models that account for divergent yield movements among different securities.

2.3. Role of Principle Component Analysis on Panel Data

Factor analysis is a dimension reduction technique with a history spanning over a century, initially introduced in the psychology literature by [25]. Principal component analysis (PCA) is a widely employed technique for identifying and estimating conventional factor models in two-dimensional panel datasets. PCA involves the extraction of latent factors and their loadings through either the singular value decomposition (SVD) of the original panel dataset, organized as a matrix, or equivalently, via the eigen decomposition of the sample covariance matrices associated with the data [26]. There are several variants of PCA that have been developed to address specific challenges or improve performance, namely Kernel PCA to address the none linearity, Incremental PCA to address the memory capacity when dealing with large datasets, Sparse PCA to address the sparsity constraint, and none stationarity time series data, Robust PCA to deal with outliers or noise and Randomized PCA to address the handle large datasets that are not possible to fit into the memory using traditional PCA and improve the sparsity and speed.

3. Methodology

Under the descriptive analysis, original data were plotted as univariate time series and examined the same with three-dimensional visualization. Correlations matrix was used to examine the intercorrelation between the rate a/ yields of different tenors (maturity period). Many scholars have identified that smoothing does a better job in yield curve modeling [27,28,29]. As per the suggestion, spline smoothing techniques were used to smooth the data (Figure 1).

4. Experiment

The analysis utilized the Treasury Bill rates for durations of 91 days, 182 days, and 364 days as the short-term rates. Meanwhile, Treasury Bond rates spanning 2 years, 3 years, 4 years, 5 years, 6 years, and 10 years were employed in the study. The dataset encompassed information from January 2010 to April 2022. The decision was made to exclude data from before 2010 due to the 30-year-long civil war that occurred in the northern and eastern regions of the country, which had a significant impact on the financial market due to external shocks. In Sri Lanka, similar to other nations, Treasury bills are structured as zero-coupon Treasury securities, while all Treasury Bonds come with bi-annual coupon payments. Daily secondary market data from the Central Bank’s public debt department, accessible via their website, served as the primary source of information for the analysis.
As per Figure 2, it is visible, that short-term yields are correlated much more strongly among them than longer yields. The Pearson correlation coefficient between 0.25 years T-Bill and 0.5 years T-Bill was 0.99 and with 1 year T-Bill was 0.98. However, the correlation coefficient between a 0.25-year T-Bill and a 10-year bond was 0.92. But the correlation coeffect between a 10-year bond and a 6-year bond was 0.99. This suggests short-term interest rates move together while longer-term interest rates move together. This further suggests the curvature structure of the yield curve.
It is learned that the main three principal components explained 0.997188 of the variation of the data (Table 3). Since the smooth data provides a higher level of variance expandability, it was decided to use the spline-smoothed data for the rest of the experiment.
It can be observed that Kernal PCA applied to functional data provides three components with the highest level of variance explained (Table 4). It is further found that the first principal component is used to explain the largest variation of the data. Despite the data exhibiting a non-stationarity, Sparse PCA that provides a remedial measure, they do not provide better results than other variants of the PCA. The 1st PCA was examined and tested with different tenors.
It was found that the 1st PCA has a substantial correlation with all the tenors of the yield curve (Table 5). So, it indicates the direction of the interest rate. Further, the highest correlation was found with a 3-year bond yield.
It was found that the 2nd PCA has a substantial correlation with gaps between two tenors, typically longer tenors and shorter tenors or medium tenors (Table 6). The strongest correlations were found with yield differences between 10-year bonds and 3-month bills. This has been visualized in Figure 3. As explained by [30], curvature is the relationship between short-intermediate and long-term yields to maturity. It is reflected in the Sri Lanka yield curve PCA as well.

5. Discussion and Conclusions

Parametric models for describing the term structure of interest rates necessitate the accurate specification of the underlying factor structure within the data. Recent research has emphasized the challenge of correctly identifying this factor space. Refs. [31,32] have demonstrated that high time-series persistence can create apparent commonality across series, suggesting the existence of a more pronounced factor structure than may actually be present. The authors of [33] have shown that even in the absence of strong serial correlation, certain characteristics of maturity-ordered assets can lead standard metrics to potentially favor a lower-dimensional representation than the true dimension of the underlying factor space [34].
In this paper, the frontier market Sri Lanka government yield curve was examined to identify the term structure of the interest. The Traditional Multivariate Principal component analysis was underperforming compared to another variant of the PCA. The study further confirmed the necessity of smoothing the data before any yield curve modeling. Despite yields behaving similarly throughout the lifespan of the pooled securities, they are not perfectly linearly associated. This allowed the use of Kernel PCA and resulted in better outcomes in explaining the variance by the first three PCAs.
The empirical studies claimed that the first three primary components’ volatilities indicate changes in the level, slope, and curvature variables, respectively, and they can be interpreted economically in useful ways. Out of the three PCAs, the first PCA is supposed to represent the long-term interest rates. In developed countries, it may represent 10-year T-Bond yields. However, this study illustrates that 1st PCA is highly correlated with the 3-year bond yield and not with the longest bond yield. This indicates that an underdeveloped frontier market yield curve direction depends on the yield of medium-term security rather than the yield of the longest-tenor security. It further highlights that liquidity, and the tenor of the security are important factors that derive the direction of the yield curve. In Sri Lanka, 3-year bond yields are more liquid throughout the longer period. Therefore, empirical results on the economic representation of 1st PCA may be different from the theoretical illustrations. The yield curve models in developed countries suggested that the 2nd PCA is associated with slop measurement, and it correlated with the yield difference of the longest tenor and medium tenor. But in Sri Lanka, it was not the yield difference of the longest tenor and medium tenor, it was the longest tenor and shortest tenor. This also suggests that the proxy for each PCA tends to change based on the level of the capital market, which is linked to the death of the bond market.
There are several ways that this study can improve or extend the scope further. Textbook descriptions of data preprocessing for PCA sometimes involves two steps: mean centering and data scaling. Whether these steps are essential depends on the specific problem and solution approach. Mean centering entails subtracting the average (of each forward rate) from the data values, effectively setting the new mean value to zero. This is particularly crucial when utilizing the Singular Value Decomposition (SVD) approach but is generally unnecessary when employing eigenvalue decomposition. Scaling involves dividing the data by the standard deviation (of each forward rate), ensuring that the new data has a standard deviation of 1.0. Scaling can be especially beneficial when the variables exhibit significantly different orders of magnitude, although this is less likely to be an issue with yield curves. If both mean centering and scaling are applied, the resulting covariance matrix will be equivalent to the correlation matrix. Some have used Logarithmic transformation in order to prevent negative interest rates. The authors of [35] examine several one- and two-factor models including LMM. The displaced logarithmic transformation has been used in such models that can be considered further.
Novel methods such as KPCA-IG and KPCA-permute [36] represent a pioneering approach within Kernel Principal Component Analysis (KPCA). It provides an efficient and robust means of data-driven feature ranking, utilizing the norm of gradient calculations. This innovation enables the identification of the most significant original variables, with no reliance on any other methods. As a result, irrelevant descriptors can be omitted, enhancing the Kernel PCA process and minimizing the potential influence of irrelevant dimensions on its similarity measure [37].

Author Contributions

Both authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Rudebusch, G.D.; Williams, J.C. Forecasting Recessions: The Puzzle of the Enduring Power of the Yield Curve, FRB of San Francisco Working Paper No. 2007-16. 2007. Available online: https://www.frbsf.org/wp-content/uploads/wp07-16bk.pdf (accessed on 30 January 2023).
  2. Puglia, M.; Tucker, A. Machine Learning, the Treasury Yield Curve and Recession Forecasting. FEDS Working Paper No. 2020-38. 2020. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3624931 (accessed on 30 January 2023).
  3. Rathnasingha, D.L.P.M.; Dayarathne, K.P.N.S. Constructing the Yield Curve for Sri Lankas Government Bond Market. International. J. Bus. Econ. Aff. 2021, 6, 56–69. [Google Scholar]
  4. Zabczyk, P.; Crump, R.K.; Moench, E. Pricing the term structure with linear regressions. J. Financ. Econ. 2013, 110, 110–138. [Google Scholar]
  5. Ferre, D.G.; Marina, E.; Raf, W. A structural decomposition of the US yield curve. J. Monet. Econ. 2009, 56, 545–559. [Google Scholar]
  6. Sekyere, A. Yield Curve Modelling: A Comparison of Principal Components Analysis and the Discrete-Time Vasicek Model. Ph.D. Thesis, Concordia University, Montreal, QC, Canada, 2019; Volume 62; pp. 25–26.
  7. Redfern, D.; McLean, D. Principal Component Analysis for Yield Curve Modeling—Reproduction of Out-of-Sample Yield Curves; Technical Report; Moody’s Analytics: New York, NY, USA, 2014. [Google Scholar]
  8. Yu, Y.; Wang, T.; Samworth, R.J. A Useful Variant of the Davis-Kahan Theorem for Statisticians. Biometrika 2015, 102, 315–323. [Google Scholar] [CrossRef]
  9. Twining, C.; Taylor, C. The use of kernel principal component analysis to model data distributions. Pattern Recognit. 2003, 36, 217–227. [Google Scholar] [CrossRef]
  10. Svensson, L. Estimating and Interpreting forward Interest Rates: Sweden 1992-4. CEPR Discussion Paper Series No 1051. 1994. Available online: https://econpapers.repec.org/paper/nbrnberwo/4871.htm (accessed on 30 January 2023).
  11. Valcu, A.; Wickens, M.R. Robustness of the three-factor model: An empirical investigation. J. Bank. Financ. 2012, 36, 2260–2273. [Google Scholar]
  12. De Pooter, M.; Martin, R.D.; Pruitt, S.W. The liquidity of automated exchanges: New evidence from German Bund futures. J. Bank. Financ. 2013, 37, 375–386. [Google Scholar]
  13. Wooldridge, J.M. Econometrics: Panel Data Methods. In Encyclopedia of Complexity and Systems Science; Meyers, R., Ed.; Springer: New York, NY, USA, 2009. [Google Scholar] [CrossRef]
  14. Estrella, A.; Trubin, M.R. The Yield Curve as a Leading Indicator: Some Practical Issues. Curr. Issues Econ. Financ. 2006, 12, 5. [Google Scholar]
  15. Karuppusami, R.; Antonisamy, B.; Premkumar, P.S. Functional principal com-ponent analysis for identifying the child growth pattern using longitudinal birth cohort data. BMC Med. Res. Methodol. 2022, 22, 76. [Google Scholar] [CrossRef]
  16. Karemaker, J.M.; Wesseling, K.H. Variability in cardiovascular control: The baroreflex reconsidered. Cardiovasc. Res. 2008, 87, 256–265. [Google Scholar] [CrossRef]
  17. Fenton, T.R.; Nasser, R.; Eliasziw, M.; Kim, J.H.; Bilan, D.; Sauve, R. Validating the weight gain of pre-term infants between the reference growth curve of the fetus and the term infant. BMC Pediatr. 2013, 13, 92. [Google Scholar] [CrossRef] [PubMed]
  18. Van Den Noort, J.C.; Ferrari, A.; Cutti, A.G.; Becher, J.G.; Harlaar, J. Gait analysis in children with cerebral palsy via inertial and magnetic sensors. Med. Biol. Eng. Comput. 2013, 51, 377–386. [Google Scholar] [CrossRef] [PubMed]
  19. Locantore, N.; Marron, J.S.; Simpson, D.G.; Tripoli, N.; Zhang, J.T.; Cohen, K.L.; Cohen, K.L. Robust principal component analysis for functional data. Test 1999, 8, 1–73. [Google Scholar] [CrossRef]
  20. Ramsay, J.O.; Dalzell, C.J. Some tools for functional data analysis. J. R Stat Soc. Ser. B Stat. Methodol. 1991, 53, 539–572. [Google Scholar] [CrossRef]
  21. Besse, P.C.; Cardot, H. Autoregressive forecasting of some functional climate variations. Scand Stat. Theory Appl. 2000, 27, 673–687. [Google Scholar] [CrossRef]
  22. Angelo, M. The Term Structure of Interest Rates: Evidence and Theory NBER Working Paper No. w1828. Available online: https://ssrn.com/abstract=227177 (accessed on 30 January 2023).
  23. Choudhry, M. Analysing and Interpreting the Yield Curve; John Wiley & Sons: Hoboken, NJ, USA, 2019. [Google Scholar]
  24. Amamiya, M. History and theories of yield curve control. In Keynote Speech at the Financial Markets Panel Conference to Commemorate the 40th Meeting; Bank of Japan: Tokyo, Japan, 2017. [Google Scholar]
  25. Spearman, C. General intelligence objectively determined and measured. Am. J. Psychol. 1904, 15, 107–197. [Google Scholar] [CrossRef]
  26. Jolliffe, I.T. Principal Component Analysis for Special Types of Data; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
  27. Chen, K.; Wu, L. The effect of smoothing on yield curve forecasting. J. Financ. Res. 2013, 36, 1–21. [Google Scholar]
  28. Wu, Y.; Zeng, Y. A comparison of smoothing methods for yield curve construction. J. Fixed Income 2011, 21, 27–42. [Google Scholar]
  29. Kim, K.H.; Lee, S.J. Yield curve modeling and forecasting: A survey. J. Financ. Econom. 2017, 15, 637–676. [Google Scholar]
  30. Kanevsk, M.; Timonin, V. Machine learning analysis and modeling of interest rate curves. In Proceedings of the 18th European Symposium on Artificial Neural Networks, Bruges, Belgium, 28–30 April 2010. [Google Scholar]
  31. Uhlig, Commenton ‘how has the Euro changed the monetary transmission mechanism?’. In NBER Macroeconomics Annual; Acemoglu, D.; Rogoff, K.; Woodford, M. (Eds.) MIT Press: Cambridge, MA, USA, 2009; Volume 24, pp. 141–152. [Google Scholar]
  32. Onatski, A.; Wang, C. Spurious factor analysis. Econometrica 2021, 89, 591–614. [Google Scholar] [CrossRef]
  33. Crump, R.K.; Gospodinov, N. On the factor structure of bond returns. Econometrica 2021, 90, 295–314. [Google Scholar] [CrossRef]
  34. Richard, K.C.; Nikolay, G. Deconstructing the Yield Curve. Federal Reserve Bank of New York Staff Reports. Available online: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr884.pdf (accessed on 30 January 2023).
  35. Gupta, A.; Subrahmanyam, M. Pricing and Hedging Interest Rate Options: Evidence from Cap-Floor Markets. J. Bank. Financ. 2005, 29, 701–733. [Google Scholar] [CrossRef]
  36. Mariette, J.; Villa-Vialaneix, N. Unsupervised multiple kernel learning for hetero-geneous data integration. Bioinformatics 2017, 34, 1009–1015. [Google Scholar] [CrossRef] [PubMed]
  37. Briscik, M.; Dillies, M.A.; Déjean, S. Improvement of variables interpretabil-ity in kernel PCA. BMC Bioinform. 2023, 24, 282. [Google Scholar] [CrossRef] [PubMed]
Engproc 68 00062 g001
Figure 1. Flow of analysis.
Figure 1. Flow of analysis.
Engproc 68 00062 g001
Engproc 68 00062 g002
Figure 2. Correlation matrix of the yields.
Figure 2. Correlation matrix of the yields.
Engproc 68 00062 g002
Engproc 68 00062 g003
Figure 3. 1st and 2nd PCA. 3rd PCA with respective yield proxies.
Figure 3. 1st and 2nd PCA. 3rd PCA with respective yield proxies.
Engproc 68 00062 g003
Table 1. Yield curve dataset.
Table 1. Yield curve dataset.
IDCalander DateTenorYield
1Jan 200891 Days T-Bill
2Feb 200891 Days T-Bill
3Jan 2008364 Days T-Bill
4Feb 2008364 Days T-Bill
Table 2. Panel version of the yield curve dataset.
Table 2. Panel version of the yield curve dataset.
IDCalander DateTenorYieldPanel
1Jan 200891 Days T-Bill 1
2Feb 200891 Days T-Bill 1
3Jan 2008364 Days T-Bill 2
4Feb 2008364 Days T-Bill 2
Table 3. Variance explained by the 1st 3 PCAs of Multivariate PCA for original and smooth data.
Table 3. Variance explained by the 1st 3 PCAs of Multivariate PCA for original and smooth data.
Data TypeP1P2P3Total Variance
Original0.972687020.019253330.004162020.99610238
Smooth0.974623670.018797410.003767480.99718856
Table 4. Variance explained by the first three PCAs of different variants of PCA.
Table 4. Variance explained by the first three PCAs of different variants of PCA.
PCA VariantP1P2P3Total Variance
Randomized PCA0.974623660.018797410.003767480.99718855
Incremental PCA0.974623360.018777710.003615490.99701656
Sparse PCA0.969000000.016000000.002000000.98700000
Functional PCA0.976700000.014800000.006600000.99810000
Kernel PCA0.976911400.018862170.004226431.00000000
Table 5. Correlation between 1st PCA and yield of different tenors.
Table 5. Correlation between 1st PCA and yield of different tenors.
3M6M12M2Y3Y4y5Y6Y10Y
0.97480.98500.98360.99120.99520.99390.99260.98570.9713
Table 6. Correlation between 2nd PCA and yield difference.
Table 6. Correlation between 2nd PCA and yield difference.
10Y-2Y10Y-3Y10Y-3M5Y-12M5Y-3M3Y-12M3Y-3M
−0.7272−0.6226−0.9526−0.8818−0.8923−0.8369−0.7270
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Dayarathne, K.P.N.S.; Thayasivam, U. Decomposing the Sri Lanka Yield Curve Using Principal Component Analysis to Examine the Term Structure of the Interest Rate. Eng. Proc. 2024, 68, 62. https://doi.org/10.3390/engproc2024068062

AMA Style

Dayarathne KPNS, Thayasivam U. Decomposing the Sri Lanka Yield Curve Using Principal Component Analysis to Examine the Term Structure of the Interest Rate. Engineering Proceedings. 2024; 68(1):62. https://doi.org/10.3390/engproc2024068062

Chicago/Turabian Style

Dayarathne, K P N Sanjeewa, and Uthayasanker Thayasivam. 2024. "Decomposing the Sri Lanka Yield Curve Using Principal Component Analysis to Examine the Term Structure of the Interest Rate" Engineering Proceedings 68, no. 1: 62. https://doi.org/10.3390/engproc2024068062

Article Metrics

Back to TopTop