How to apply the novel dynamic ARDL simulations (dynardl) and Kernel-based regularized least squares (krls)

Abstract

The application of dynamic Autoregressive Distributed Lag (dynardl) simulations and Kernel-based Regularized Least Squares (krls) to time series data is gradually gaining recognition in energy, environmental and health economics. The Kernel-based Regularized Least Squares technique is a simplified machine learning-based algorithm with strength in its interpretation and accounting for heterogeneity, additivity and nonlinear effects. The novel dynamic ARDL Simulations algorithm is useful for testing cointegration, long and short-run equilibrium relationships in both levels and differences. Advantageously, the novel dynamic ARDL Simulations has visualization interface to examine the possible counterfactual change in the desired variable based on the notion of ceteris paribus. Thus, the novel dynamic ARDL Simulations and Kernel-based Regularized Least Squares techniques are useful and improved time series techniques for policy formulation.•We customize ARDL and dynamic simulated ARDL by adding plot estimates with confidence intervals.•A step-by-step procedure of applying ARDL, dynamic ARDL Simulations and Kernel-based Regularized Least Squares is provided.•All techniques are applied to examine the economic effect of denuclearization in Switzerland by 2034.

Keywords: Average marginal effects; Counterfactual change; Dynamic autoregressive distributed lag simulations; Dynardl; Impulse-Response; Kernel-based regularized least squares; Krls; Pointwise derivatives; Response surface regressions; time series techniques.

Graphical abstract

Scheme 1

Salient steps in applying the dynamic ARDL simulations.

Fig. 1

Parameter estimates of the ARDL model. Notes: black (●) is the estimate in a log-log model, olive teal long-dash 3-dots is the reference line, red-spike denotes lower 95% and upper 95% confidence limit. Legend: GFCF represents Gross Fixed Capital Formation, LABOR represents labor, EXPORTS denotes exportation of goods and services from Switzerland, and NUKE means consumption of nuclear energy. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2

Standardized normal probability plot.

Fig. 3

Quantiles of residuals against quantiles of normal distribution.

Fig. 4

Cumulative sum test using OLS CUSUM plot for parameter stability.

Fig. 5

Parameter estimates of dynamic ARDL Simulations. Notes: black (×) is the estimate in a log-log model, olive teal long-dash 3-dots is the reference line, red-spike denotes lower 95% and upper 95% confidence limit. Legend: GFCF represents Gross Fixed Capital Formation, LABOR represents labor, EXPORTS denotes exportation of goods and services from Switzerland, and NUKE means consumption of nuclear energy. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6

Representation of counterfactual shock in predicted nuclear energy using dynamic ARDL simulations. Notes: black dot (●) is the predicted GDP by −21% shock in nuclear energy in a log-log model; olive teal, red and light-blue spikes denote 75, 90, and 95% confidence interval. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7

Representation of Pointwise marginal effect of nuclear energy.