The Cusum Test for Parameter Change in Regression with ARCH Errors

In this paper, we concentrate ourselves on Inclán and Tiao (1994)'s cusum test in regression models with ARCH errors. The ARCH and GARCH models have long been popular in financial time series analysis. For a general review, see Gouriéroux (1997).Inclán and Tiao (1994)'s cusum test was originally designed for testing for variance changes and allocating their locations in iid samples. Later, it was demonstrated that the same idea can be extended to a large class of time series models (cf. Lee et all, 2003(a)). Also, the variance change test has been studied in unstable AR models (cf. Lee et al. (2003(b)). In fact, Kim, Cho and Lee (2000) considered to apply the cusum test to GARCH(1,1) models taking account of the fact that the variance is a functional of GARCH parameters, and their change can be detected by examining the existence of the variance change. Although this reasoning was correct, it turned out that the cusum test suffers from severe size distortions and low powers. Hence, there was a demand to improve their cusum test. Here, in order to circumvent such drawbacks, we propose to use the cusum test based on the residuals, given as the squares of observations divided by estimated conditional variances. We intend to use residuals since the residual based test conventionally discard correlation effects and enhance the performance of the test. In fact, a significant improvement was observed in our simulation study. Despite the previous work of Lee et al. (2003(b)) also considers a residual cusum test in time series models, the model of main concern was the autoregressive model with several unit roots. In fact, the mathematical analysis of the cusum test heavily relies on the probabilistic structure of the underlying time series model, and the arguments used for establishing the weak convergence result in unstable models are somewhat different from those in ARCH models. Therefore it is worth to investigate the asymptotic behavior of the residual cusum test in ARCH models. Although the present paper was originally motivated to improve Kim, Cho and Lee (2000)'s test in the GARCH(1,1) model, we consider the cusum test in a more general class of models including regression models with infinite order ARCH errors.Test for parameter change, regression models with ARCH errors, residual cusum test, Brownian bridge, weak convergence

Statistical Software for State Space Methods

In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.

Vector AR Implementation for Rain Rate Space Time Series Modeling in Surabaya

Site diversity is one of the Fading Mitigation Techniques (FMT) that is a base system design on the nature of rain rate that change to the time and space. However, to get appropriate site diversity needs deep knowledges about rain rate dynamic and statistical characteristic. In this research, rain rate space-time series modeling in 4 rain gauges location studied by using Vector AR (VAR) model. To validate VAR model, it used 3 methods; ecdf graphic comparison, qqplot method and model residual analysis. The result showed that VAR model is correct and appropriate model for rain rate space time series modeling in 4 rain gauges location. These VAR models have good accuracy with Spatial RMSE Mean between 0.273 - 0.763

Ski areas, weather and climate: Time series models for New England case studies

Wintertime warming trends experienced in recent decades, and predicted to increase in the future, present serious challenges for ski areas and whole regions that depend on winter tourism. Most research on this topic examines past or future climate-change impacts at yearly to decadal resolution, to obtain a perspective on climate-change impacts. We focus instead on local-scale impacts of climate variability, using detailed daily data from two individual ski areas. Our analysis fits ARMAX (autoregressive moving average with exogenous variables) time series models that predict day-to-day variations in skier attendance from a combination of mountain and urban weather, snow cover and cyclical factors. They explain half to two-thirds of the variation in these highly erratic series, with no residual autocorrelation. Substantively, model results confirm the backyard hypothesis that urban snow conditions significantly affect skier activity; quantify these effects alongside those of mountain snow and weather; show that previous-day conditions provide a practical time window; find no monthly effects net of weather; and underline the importance of a handful of high-attendance days in making or breaking the season. Viewed in the larger context of climate change, our findings suggest caution regarding the efficacy of artificial snowmaking as an adaptive strategy, and of smoothed yearly summaries to characterize the timing-sensitive impacts of weather (and hence, high-variance climate change) on skier activity. These results elaborate conclusions from our previous annual-level analysis. More broadly, they illustrate the potential for using ARMAX models to conduct integrated, dynamic analysis across environmental and social domains

One Fits All:Power General Time Series Analysis by Pretrained LM

Although we have witnessed great success of pre-trained models in natural language processing (NLP) and computer vision (CV), limited progress has been made for general time series analysis. Unlike NLP and CV where a unified model can be used to perform different tasks, specially designed approach still dominates in each time series analysis task such as classification, anomaly detection, forecasting, and few-shot learning. The main challenge that blocks the development of pre-trained model for time series analysis is the lack of a large amount of data for training. In this work, we address this challenge by leveraging language or CV models, pre-trained from billions of tokens, for time series analysis. Specifically, we refrain from altering the self-attention and feedforward layers of the residual blocks in the pre-trained language or image model. This model, known as the Frozen Pretrained Transformer (FPT), is evaluated through fine-tuning on all major types of tasks involving time series. Our results demonstrate that pre-trained models on natural language or images can lead to a comparable or state-of-the-art performance in all main time series analysis tasks, as illustrated in Figure 1. We also found both theoretically and empirically that the self-attention module behaviors similarly to principle component analysis (PCA), an observation that helps explains how transformer bridges the domain gap and a crucial step towards understanding the universality of a pre-trained transformer.The code is publicly available at https://github.com/DAMO-DI-ML/One_Fits_All.Comment: Neurips 2023 Spotligh

Semiparametrically Efficient Inference Based on Signs and Ranks for Median Restricted Models

Since the pioneering work of Koenker and Bassett (1978), econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest.Contrary to the traditional models where the noise is assumed to have mean zero, median-restricted models enjoy a rich group-invariance structure.In this paper, we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models.These procedures are based on residual signs and ranks, and therefore insensitive to possible misspecification of the underlying innovation density, yet semiparametrically efficient at correctly specified densities.This latter combination is a definite advantage of these procedures over classical quasi-likelihood methods.The techniques we propose can be applied, without additional technical difficulties, to both cross-sectional and time-series models.They do not require any explicit tangent space calculation nor any projections on these.models;regression analysis;econometrics

Time Series Modelling of Monthly WTI Crude Oil Returns

This paper examines the dynamics of the monthly WTI crude oil return for the past two decades. The data are divided into two ten-year periods, and we explore with two approaches. We rst build univariate time series models using the Box-Jenkins methodology. Techniques such as stationarity tests and autocorrelation plots are used to determine the orders of the nal ARIMA model. GARCH and APARCH are also used to model residuals. Then, we build regression models based on eight explanatory variables. They are consumption, production, ending stock, net import, renery utilisation rate, U.S. interest rate, NYMEX oil futures contract 4 and S&P 500 index. Stepwise AIC method is employed to determine the optimal variables to be included. Multicollinearity is not evident in the reduced models. Residual analysis suggests that the assumptions of linear regression are not violated. Lastly, the forecasting powers of the models are compared. GARCH and APARCH perform the best in terms of forecasting accuracy, with APARCH performing the best in a turbulent market.\ud \ud Keywords: Linear regression, ARIMA, GARCH, APARCH, time series forecasting, residual analysi

The Gaussian graphical model in cross-sectional and time-series data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in 3 kinds of psychological datasets: datasets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered datasets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means---the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.Comment: Accepted pending revision in Multivariate Behavioral Researc