A Monte Carlo Simulation Analysis of the NARDL Method with Regard to CryptocurrenciesAbdülsamet Aça, Kemal Dinçer Dingeç
One of the nonlinear techniques utilized in the analysis of economic and financial variables is the nonlinear autoregressive distributed lag (NARDL) method. This study primarily focuses on the NARDL approach, which offers the chance to assess the asymmetric relationships between cryptocurrencies and economic and financial variables. Monte Carlo experiments were carried out while developing the NARDL method for the purpose of investigating the finite sample properties of estimators under the premise of normal distribution for a simple data generation procedure. This study examines the NARDL method’s dependability for non-normal distributions. The return distributions of cryptocurrencies are obviously non-normal and heavy-tailed, making this a significant research challenge. This study simulates the NARDL model using both several heavy-tailed distributions as well as a normal distribution. To the best of our knowledge, no research has yet occurred on the NARDL method’s finite sample qualities for time series with non-normality. The findings from this study could have a significant impact on how accurately predictions are made regarding the impact cryptocurrencies have on the economy and finance.
NARDL Yönteminin Kripto Para Birimlerine Yönelik Bir Monte Carlo Simülasyon AnaliziAbdülsamet Aça, Kemal Dinçer Dingeç
Doğrusal olmayan ARDL (NARDL) yöntemi ekonomik ve finansal değişkenlerin incelenmesinde kullanılan doğrusal olmayan ekonometrik yöntemlerden biridir. Kripto paralar ile ekonomik ve finansal değişkenler arasındaki asimetrik ilişkileri inceleme imkânı sunan NARDL yöntemi bu çalışmanın odak noktasını oluşturmaktadır. NARDL metodunun ilk geliştirilme aşamasında, tahmin edicilerin sonlu örnek özelliklerini araştırmak için basit veri üretme süreci kullanılarak ve normal dağılım varsayımı altında Monte Carlo deneyleri yapılmıştır. Bu çalışmada ise NARDL yönteminin güvenilirliği normal olmayan dağılımlar altında incelenmektedir. Kripto para birimlerinin getiri dağılımları normal dağılımından farklı ve de ağır kuyruklu olduğu için bu önemli bir araştırma problemidir. Bu çalışmada, NARDL modeli normal dağılım ve farklı ağır kuyruklu dağılımlar (Student t-dağılımı ve Skew-t dağılımı) altında simüle edilmiştir. Literatürde, bildiğimiz kadarıyla, normal olmayan zaman serileri için NARDL yönteminin sonlu örnek özellikleri üzerine bir çalışma bulunmamaktadır. Bu açıdan çalışmamızın sonuçları, kripto para birimlerinin ekonomi ve finans üzerindeki etkileri hakkında yapılan değerlendirmelerin doğruluğu üzerine çıkarımlar yapılmasında yol gösterici olacaktır.
Investor interest in cryptocurrencies increased after Nakatomo’s (2008) suggestion of Bitcoin. The presence and usefulness of cryptocurrencies in economic and financial systems are continually growing, and this has drawn attention from academicians. Several studies on cryptocurrencies have been carried out in recent years. Between 2013 and 2019, Corbet et al. (2019) conducted a thorough assessment of quantitative and non-quantitative studies on cryptocurrencies. Quantitative studies have investigated the relationships among numerous variables (e.g., Bitcoin returns, altcoin investments, gold prices, oil prices, etc.) using a variety of approaches such as regression models, vector error correction models, generalized autoregressive conditional heteroskedasticity (GARCH), autoregressive distributive lag (ARDL), and correlation analyses. The studies conducted prior to 2020 used linear methods to explore the relationships among variables, while some studies since 2020 have also used nonlinear methods. This study uses Student’s t-distribution and skewed t-distributions, as well as a normal distribution, to simulate the nonlinear ARDL [NARDL] model. The return distributions of cryptocurrencies are obviously non-normal and heavy-tailed, making this a significant research problem. Shanaev and Ghimire (2021) applied the Cramer-von Mises, Anderson-Darling, Kuiper, Kolmogorov-Smirnov, and chi-squared goodness-of-fit tests for 22 different theoretical distributions to determine the distributions for 772 different cryptocurrencies. In addition to a normal distribution, they found cryptocurrencies to have non-normal distributions such as Student’s t-distribution, skewed-t distribution, Johnson SU distribution, and asymmetric power function distribution.
Developed by Shin et al. (2014), the NARDL model is an enhanced version of the ARDL model. Developed by Pesaran et al. (2001), the ARDL model is a cointegration analysis that is used to detect long- and short-term causality relationships between non-stationary series at different levels. One important feature of this cointegration analysis is that it does not require the series to have the same order. The purpose of creating the NARDL model is to develop a simple flexible nonlinear dynamic framework that can simultaneously and consistently model both long-term relationships among variables as well as the asymmetries in dynamic fit models. The NARDL approach constitutes a nonlinear modeling technique that is employed to examine economic and financial factors. The present study focuses on employing the ARDL technique, which offers a means of examining the non-reciprocal associations cryptocurrencies have with economic and financial variables. In order to investigate the finite sample properties of estimators for the simple data generation process, Shin et al. (2014) used Monte Carlo simulation experiments. To the best of our knowledge, no scholarly publication has been encountered that has conducted an investigation into the finite sample properties of the NARDL method when applied to time series data with non-normal distribution. During the Monte Carlo simulation experiments, hypothesis tests were conducted for the finite sample properties of the estimators, as well as for long-term asymmetric relationships, short-term asymmetric relationships, and non-asymmetric cointegration. The size and powers of the hypothesis theses have been examined under normal and non-normal distributions.
The default parameter values for the Monte Carlo simulation experiments under normal distribution were taken as excerpts from Shin et al. (2014), while we created the default values for the Student’s t-distribution and the skewed-t distribution. The Monte Carlo simulation experiments were performed by utilizing Shin et al.’s error correction model. The Monte Carlo simulation experiments were conducted using the software programs STATA and R.
The results from the Monte Carlo simulations show the size of the NARDL model for the normal distribution and for the Student’s t-distribution to decrease and its power to increase as the number of samples increases. The study has also revealed that a variable with a skewed-t distribution possessing a skewness value of -2, 2.1 degrees of freedom, and a correlation value of -0.5 would not accurately show the short-term asymmetric relationship if its relationship with other variables is examined using NARDL.When the degrees of freedom are increased to 3, or 10 for the mentioned skewed-t distribution, the Wald test has moderate power over the short term.
In this respect, the results from our study shows the studies that have used the NARDL model for evaluating the effects of cryptocurrencies on economics and finance to be predominantly reliable and accurate. Only one contrary finding was found where the skewed-t distribution possessed a very high kurtosis value and a high positive skewness value. For this case, the Wald test was observed to have very low power regarding the short-term asymmetric relationship.