Identifying the Most Relevant Lag with Runs

Úrsula Faura,Mariano Matilla-García,Matilde Lafuente,Manuel Ruiz

doi:10.3390/e17052706

Abstract

In this paper, we propose a nonparametric statistical tool to identify the most relevant lag in the model description of a time series. It is also shown that it can be used for model identification. The statistic is based on the number of runs, when the time series is symbolized depending on the empirical quantiles of the time series. With a Monte Carlo simulation, we show the size and power performance of our new test statistic under linear and nonlinear data generating processes. From the theoretical point of view, it is the first time that symbolic analysis and runs are proposed to identifying characteristic lags and also to help in the identification of univariate time series models. From a more applied point of view, the results show the power and competitiveness of the proposed tool with respect to other techniques without presuming or specifying a model.

Highlights

In this paper, we are interested in providing new statistical tools that help in the process of modelling univariate time series processes
The paper shows that the new approach can be useful for model identification, and it is applied to the a real time series, to the New York Stock Exchange
The results provided for data generating processes (DGPs) 7 allows to understand that to fail to detect the most relevant lag parameter(s) is equivalent to find that all considered lags are important, that is to say, δ = τ1, where τ is the number of lags that the user has considered in the study

Summary

Introduction

We are interested in providing new statistical tools that help in the process of modelling univariate time series processes. Autocorrelation and partial autocorrelation coefficients have been utilized by empirical modellers in specifying the appropriate delays It is well established [1] that processes with zero autocorrelation could still exhibit high order dependence or nonlinear time dependence. The vast majority of these statistical tests are of nonparametric nature, trying to avoid restrictive assumptions on the marginal distributions of the model These tests are not designed for selecting relevant lags. This partly explains the relative scarcity of nonparametric techniques for investigating lag dependence, regardless the linear or nonlinear nature of the process, which is an aspect that is unknown in most of the practical cases. We construct a new nonparametric runs statistic, based on symbolic analysis, which estimates the lag that best describes a time series sample. The paper shows that the new approach can be useful for model identification, and it is applied to the a real time series, to the New York Stock Exchange

Definitions and Notation

Constructing the Statistic

Monte Carlo Simulation Experiments

Model Identification

Findings

Conclusions