Time-Series Analysis General Purpose and Description

Evidently, many economic variables show some sort of trending behavior, whether it be the gross domestic product or a stock market index. Typically, for these cases time-series modelling under the assumption of stationarity or forecasting by extrapolation using time-constant means would be highly implausible. Other variables, such as inflation and unemployment rates, show rising or falling trends over longer time spans, but extrapolating these trends may be of doubtful value for modelling.

The Quarterly Review of Economics and Finance, 1996

2017

The pace of developments in econometrics has made it increasingly difficult for students and professionals alike to be aware of what is important and likely to be lasting in theory and practical applications. This series addresses important key developments within a unified framework, with individual volumes organised thematically. The series is relevant for both students and professionals who need to keep up with the econometric developments, yet is written for a wide audience with a style that is designed to make econometric concepts available to economists who are not econometricians.

Agricultural and Forest Meteorology, 1999

The presence of autocorrelation in the analysis of a variable sampled sequentially at regular time intervals appears to be unknown to many agricultural meteorologists despite abundant documentation found in the traditional meteorological and statistical literature. It follows that the statistical consequences as well as methodological alternatives are also unknown. Through an example using paired radiometer observations, this note discusses recognition of autocorrelation as well as the importance of testing ordinary least squares regression parameters in the presence of autocorrelated residuals. An autoregression example is presented as one alternative way to analyze the given dataset. # 0168-1923/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 -1 9 2 3 ( 9 9 ) 0 0 0 2 5 -8

Time series econometrics is a rapidly evolving field. In particular, the cointegration revolution has had a substantial impact on applied analysis. As a consequence of the fast pace of development, there are no textbooks that cover the full range of methods in current use and explain how to proceed in applied domains. This gap in the literature motivates the present volume. The methods are sketched out briefly to remind the reader of the ideas underlying them and to give sufficient background for empirical work. The volume can be used as a textbook for a course on applied time series econometrics. The coverage of topics follows recent methodological developments. Unit root and cointegration analysis play a central part. Other topics include structural vector autoregressions, conditional heteroskedasticity, and nonlinear and nonparametric time series models. A crucial component in empirical work is the software that is available for analysis. New methodology is typically only gradually incorporated into the existing software packages. Therefore a flexible Java interface has been created that allows readers to replicate the applications and conduct their own analyses.

2009

International Journal of Forecasting, 2004

Applied Time Series Modelling and Forecasting provides a non-technical approach to applied econometric time series models, which involve non-stationary data. This monograph emphasizes the why and how of econometric time series modeling and places less emphasis on the analytical details. Additionally, it extends the topical coverage of Harris (1995) by discussing the econometric analysis of panel tests for unit tests and co-integration as well as for financial time series data. Additionally, the authors present the latest techniques in structural breaks and season unit root testing, testing co-integration with a structural break, seasonal co-integration in multivariate models, and approaches to structural macroeconomic modeling. Chapter 1 provides an overview (or review for some readers) of the basic analytics of time series analysis, which provides the foundation for the remainder of the monograph. Chapter 2 includes details of short-and long-run relationships of the time series, with the first part of the chapter focusing on the examination of long-run relationships between the economic time series. Moreover, the discussion delves into distinguishing between stationary and non-stationary variables. Neglecting to examine such distinctions could result in a spurious regression, which might imply a statistically significant long-run relationship when no causal relationship exists. In fact, the establishment of a long-run relationship naturally leads to the concept of co-integration, which allows analysts to examine if there is a causal relationship between the economic time series. The final part studies the short-run relationships of economic time series. The discussion stresses that the estimation of short-run models can be problematic and argues that the method of differencing the data is not a good solution since this would remove information about the long-run behavior of the time series. Thus, a remedy would be the error correction model (ECM) since the ECM would contain information about the long-and short-run aspects of the economic time series. Chapter 3 presents the details of the presence of a unit root in the time series, and the discussion begins with the Dickey -Fuller (DF) test for a unit root showing that a t-test of the null hypothesis of nonstationarity is not based on the standard t-distribution. Much of the discussion deals with what elements should be included in the testing procedure. That is, whether the inclusion of the trend and the intercept (i.e., deterministic components) or just one of them would result in different results in the testing procedure. The chapter continues by going into the issues of which of the deterministic components should enter the testing process by examining a sequential testing procedure espoused by Perron. The Dickey -Fuller test is modified to examine a more complicated time series known as the augmented Dickey-Fuller, one that entails the addition of lagged dependent variables to the test equation. The discussion continues with the issues of how many lagged terms should be incorporated into the test and related issues such as the power and size properties of the augmented Dickey -Fuller test. The final part of the chapter discusses the empirical issues of seasonal unit roots, including the integration of structural breaks. Chapters 4 and 5 provide a discussion of the estimation of co-integration of single equation models (Chapter 4) and multiple co-integration models (Chapter 5). The most commonly applied method in testing for co-integration, up to the early 1990s, was the twostep estimation procedure of Engle and Granger (1987). This single-equation method for estimation of co-integration is based on the restrictive assumption of a single co-integration relationship, which is estimated via the OLS procedure. However, with the case of more 0169-2070/$ -see front matter D

American Journal of Mathematics and Statistics, 2016

Regression model assumes that the error terms are non-correlated. This is not always true with time series data as observations at one point in time often tend to be correlated with nearby observations. Durbin Watson test was carried out to determine whether or not the error terms are autocorrelated. Where autocorrelation existed, various models for estimating time series with autocorrelation were employed to model the series. The models used are Autoregressive model (AR), Moving Average model (MA), The Autoregressive Moving Average model (ARMA) and Integrated Moving Average model (ARIMA). These models were used on the exchange rate of Naira per Dollar at various market segments and then compared using the standard error and the ratio of coefficient to standard error criteria to obtain the model that best fit. Results however suggest that mixed models at smaller lags should often be adopted in modeling financial time series with evidence of autocorrelated error terms.

This paper explains in detail basic procedure how to analyze the data using Autoregressive Integrated Moving Average analysis (ARIMA). The paper consists of two parts and appendix. Computational basis of ARIMA analysis are covered in the first part, while practical applications (worked examples) and interpretation of the results, were covered in the second part. The appendix contains programing code needed to analyze the data written R-language and the links to the data sets used in this paper. In order to fully utilize this paper, the reader should be familiar with the R-language and mathematical (theoretical) basis of ARIMA analysis.

Academic Press, Inc. eBooks, 2000

Chapter 2 Extrapolative and Decomposition Models 2.1. Introduction 15 vii viii Contents 2.2. Goodness-of-Fit Indicators 15 2.3. Averaging Techniques 18 2.3.1. The Simple Average 18 2.3.2. The Single Moving Average 18 2.3.3. Centered Moving Averages 20 2.3.4. Double Moving Averages 20 2.3.5. Weighted Moving Averages 22 2.6. New Features of Census X-12 66 References 66 References 99 Chapter 4 The Basic ARIMA Model 4.1. Introduction to ARIMA 101 4.2. Graphical Analysis of Time Series Data 102 4.2.1. Time Sequence Graphs 102 4.2.2. Correlograms and Stationarity 106 4.3. Basic Formulation of the Autoregressive Integrated Moving Average Model 108 4.4. The Sample Autocorrelation Function 110 4.5. The Standard Error of the ACF 4.6. The Bounds of Stationarity and Invertibility 4.7. The Sample Partial Autocorrelation Function 4.7.1. Standard Error of the PACF 4.8. Bounds of Stationarity and Invertibility Reviewed 4.9. Other Sample Autocorrelation Functions 4.10. Tentative Identification of Characteristic Patterns of Integrated, Autoregressive, Moving Average, and ARMA Processes

Time Series Homework2 0352618 張奕得 2.1 (a) According to the code, we have the table: Before I interpret, we notice that if the model is correct, the covariates are all significant and fit quite well by p-values and adjusted . That is we capture most variation by the variables. Top-to-bottom are estimate of respectively.