Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes
Abstract
:1. Introduction and Problem Statement
1.1. Introduction and Motivation
- is the long-term equilibrium value about which the process performs random excursions;
- represents the elastic spring constant that determines how fast random excursions will revert back to the central attractor (a). Large values for k imply a tightly bound process resulting in short excursions;
- is the (specific) volatility;
- measures the sensitivity of the volatility with respect to the current process value.
1.2. Problem Statement
1.3. Overview of the Methodology
- We were interested in finding out whether the down-swing around observation 3000 (which corresponds to a period in 2008–2009) is unusual. Since this period comprises 100–200 daily observations, we picked a convolution filter () of size .
- The response (in absolute value) of the original data after convolution with is shown in the bottom panel of Figure 2 in Section 4.1.1. Clearly the most vigorous response occurred around location 3000. However, in and of itself this does not prove anything. The question is whether this response is unusually high.
- To proceed, we first defined a single number to express the size of the maximum response relative to a statistically stable response measure, e.g., the 90%-percentile of the response values (indicated by the red line in the bottom panel of Figure 2 in Section 4.1.1). We denoted the resulting value by , which, for the oil data, turns out to be 3.82.
- Next, we needed to decide whether this observed value for T is exceptional. We assumed that the dynamics underlying the observed time series were indeed governed by a CKLS process, estimated its parameters from the observed data sequence and used the results to generate a large number of simulated sample paths. For each of these simulated sample paths, we computed the corresponding T statistic. This allowed us to estimate the p-value of under the assumption of CKLS dynamics.
- Finally, since we know that the estimated CKLS parameters used to generate sample paths are subject to a considerable amount of uncertainty, we repeated the simulation experiments for a range of likely parameter values. This told us how sensitive our conclusions were to changes in the parameter values, and whether they would hold up if the parameters had slightly different values.
2. Data
- Oil Price (West Texas Intermediate) over the period 2000 to 2018 (see Figure 2, top panel in Section 4.1.1): This series comprises 6575 daily observations. The evolution of the oil price showed some sharp downward jumps. This begs the question: is this perceived discontinuity part of the natural evolution of an appropriate CKLS process or does it correspond to an (exogenous) shock?
- US Interest Rate (see Figure 5, top panel in Section 4.2) over the period 1972 to 2018. This series comprises 16,816 daily observations and shows a conspicuous dip around observation 7000. Again, the question is whether this is unexpected given an appropriate CKLS model.
3. Related Work
4. Methodology and Results
4.1. Oil Price Data
4.1.1. Computing the Test Statistic
4.1.2. Using Monte Carlo to Compute the p-Value of the Test Statistic
4.1.3. Sensitivity of the p-Value
4.1.4. Corroborating the Choice of Filter Size (r)
4.2. US Interest Rate (1972–2018)
5. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
BM | Brownian motion |
CKLS | Chan, Karolyi, Longstaff, and Sanders (process) |
GMM | Generalized Method of Moments |
MC | Monte Carlo (estimation) |
SDE | Stochastic Differential Equation |
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Parameter | ||||
---|---|---|---|---|
value | 0.35 | 67.1 | 1.24 | 0.69 |
Parameter | ||||
---|---|---|---|---|
value | 0.15 | 4.47 | 0.24 | 1.13 |
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Kokabisaghi, S.; Pauwels, E.J.; Van Meulder, K.; Dorsman, A.B. Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes. Int. J. Financial Stud. 2018, 6, 76. https://doi.org/10.3390/ijfs6030076
Kokabisaghi S, Pauwels EJ, Van Meulder K, Dorsman AB. Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes. International Journal of Financial Studies. 2018; 6(3):76. https://doi.org/10.3390/ijfs6030076
Chicago/Turabian StyleKokabisaghi, Somayeh, Eric J. Pauwels, Katrien Van Meulder, and André B. Dorsman. 2018. "Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes" International Journal of Financial Studies 6, no. 3: 76. https://doi.org/10.3390/ijfs6030076
APA StyleKokabisaghi, S., Pauwels, E. J., Van Meulder, K., & Dorsman, A. B. (2018). Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes. International Journal of Financial Studies, 6(3), 76. https://doi.org/10.3390/ijfs6030076