This paper studies the random walk, in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).

/pdf/time-series-regression-with-a-unit-root-2czgv7ji3h.pdf

Time series regression with a unit root

Trends and random walks in macroeconomic time series: Further evidence from a new approach

This book provides a wide-ranging account of the literature on co-integration and the modelling of integrated processes (those which accumulate the effects of past shocks). Data series which display integrated behaviour are common in economics, although techniques appropriate to analysing such data are of recent origin and there are few existing expositions of the literature. This book focuses on the exploration of relationships among integrated data series and the exploitation of these relationships in dynamic econometric modelling. The concepts of co-integration and error-correction models are fundamental components of the modelling strategy. This area of time-series econometrics has grown in importance over the past decade and is of interest to econometric theorists and applied econometricians alike. By explaining the important concepts informally, but also presenting them formally, the book bridges the gap between purely descriptive and purely theoretical accounts of the literature. The asymptotic theory of integrated processes is described and the tools provided by this theory are used to develop the distributions of estimators and test statistics. Practical modelling advice, and the use of techniques for systems estimation, are also emphasized. A knowledge of econometrics, statistics, and matrix algebra at the level of a final-year undergraduate or first-year undergraduate course in econometrics is sufficient for most of the book. Other mathematical tools are described as they occur.

Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data

Box & Cox (1964) proposed a parametric power transformation technique in order to reduce anomalies such as non-additivity, non-normality and heteroscedasticity. Although the transformation has been extensively studied, no bibliography of the published research exists at present. An attempt is made here to review the work relating to this transformation.

/pdf/the-box-cox-transformation-technique-a-review-541fsqfgr6.pdf

The Box-Cox transformation technique: a review

This paper deals with the estimation of unequally spaced panel data regression models with AR(1) remainder disturbances. A feasible generalized least squares (GLS) procedure is proposed as a weighted least squares that can handle a wide range of unequally spaced panel data patterns. This procedure is simple to compute and provides natural estimates of the serial correlation and variance components parameters. The paper also provides a locally best invariant test for zero first-order serial correlation against positive or negative serial correlation in case of unequally spaced panel data.

/pdf/unequally-spaced-panel-data-regressions-with-ar-1-2i9h0qr479.pdf

Unequally spaced panel data regressions with ar(1) disturbances

Recent studies by Durbin and Watson [5], L'Esperance and Taylor [10], Koerts and Abrahamse [8], Tillman [15], Vinod [16], Savin and White [14] and others have shown increasing interest in the test of autocorrelation based on the d statistic proposed by Durbin and Watson [3 and 4]. The focus of these papers has been the computation of the exact distribution of d and the power of the test based on d. The exact distribution of d has been developed by Imhof [7] and Pan Jie-Jian [12]. However, few of the generally available computer programs for regression analysis incorporate these methods,2 possibly because of computational costs, particularly for large samples. With the Durbin and Watson [4] tables the bounds test is restricted to time series regressions with 15 to 100 observations and a maximum of 5 regressors in addition to unity. Often regression studies do not meet these restrictions since samples with less than 15 observations commonly occur with annual time series and regressions with more than 5 regressors are often found in the context of simultaneous equations and of distributed lags.3 In this paper we present extended tables for the bounds test. Our tables can be used for samples with 6 to 200 observations and for as many as 20 regressors.

The durbin-watson test for serial correlation with extreme sample sizes or many regressors'

Estimation and testing for functional form and autocorrelation: A simultaneous approach

Testing for Autocorrelation with Missing Observations

Testing the autoregressive parameter with the t statistic

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

N. E. Savin

Author Tools

Chat about Author

Papers

The durbin-watson test for serial correlation with extreme sample sizes or many regressors'

Estimation and testing for functional form and autocorrelation: A simultaneous approach

Testing for Autocorrelation with Missing Observations

Testing the autoregressive parameter with the t statistic