scholarly journals The Size‐Power Tradeoff in HAR Inference

Econometrica ◽  
2021 ◽  
Vol 89 (5) ◽  
pp. 2497-2516 ◽  
Author(s):  
Eben Lazarus ◽  
Daniel J. Lewis ◽  
James H. Stock
Keyword(s):  
Time Series ◽  
Closed Form ◽  
Kernel Estimation ◽  
Rejection Rate ◽  
Critical Values ◽  
Conventional Wisdom ◽  
Time Series Regression ◽  
Truncation Parameter ◽  
Long Run ◽  
Multivariate Location

Heteroskedasticity‐ and autocorrelation‐robust (HAR) inference in time series regression typically involves kernel estimation of the long‐run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test's null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher‐order expansions, we provide a unified size‐power frontier for both kernel and weighted orthonormal series tests using nonstandard “fixed‐ b” critical values. We also provide a frontier for the subset of these tests for which the fixed‐ b distribution is t or F. These frontiers are respectively achieved by the QS kernel and equal‐weighted periodogram. The frontiers have simple closed‐form expressions, which show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.

scholarly journals Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown

1994 ◽  
Vol 10 (3-4) ◽  
pp. 672-700 ◽  
Author(s):  
Graham Elliott ◽  
James H. Stock
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Critical Values ◽  
Asymptotic Power ◽  
Time Series Regression ◽  
Second Stage ◽  
Alternative Approach ◽  
Local Asymptotic Power ◽  
Size Distortions ◽  
Correct Size

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible situations. We then propose an alternative approach in which the second-stage critical values depend continuously on a first-stage statistic that is informative about the order of integration of the regressor. This procedure has the correct size asymptotically and good local asymptotic power.

Long-run equity performance of firms that restate financial statements

2019 ◽  
Vol 46 (1) ◽  
pp. 92-108
Author(s):  
Gisung Moon ◽  
Hongbok Lee ◽  
Doug Waggle
Keyword(s):  
Time Series ◽  
Factor Model ◽  
Abnormal Returns ◽  
Financial Statements ◽  
Regression Analyses ◽  
Time Series Regression ◽  
Content Type ◽  
Long Run ◽  
Abnormal Performance ◽  
Three Factor

Purpose The authors investigate how the stock market reacts to financial restatements using the restatements data from the United States Government Accountability Office (GAO-06-678). In particular, the purpose of this paper is to examine the long-run equity performance of the restating firms, for holding periods of one to five years after the announcements of restatements. Design/methodology/approach This paper measures the long-run stock performance of restating firms with the buy-and-hold abnormal returns and time-series regression analyses based on Fama–French’s (1993) three-factor model and Carhart’s (1997) four-factor model. Findings The authors find that restating firms significantly underperform in the long run compared with their peers matched by industry, size and book-to-market. Restating firms’ underperformance is confirmed with time-series regression analyses based on Fama–French’s (1993) three-factor model and Carhart’s (1997) four-factor model. Further, the authors find the negative long-run abnormal performance of restating firms is primarily driven by large firms. The authors also report that self-prompted restatements and improper revenue accounting-triggered restatements result in worse long-run abnormal performance. Originality/value This paper is the first paper that thoroughly investigates the long-run stock returns of the firms that restate financial statements by fully considering the size effect.

HETEROSKEDASTICITY AUTOCORRELATION ROBUST INFERENCE IN TIME SERIES REGRESSIONS WITH MISSING DATA

2018 ◽  
Vol 35 (03) ◽  
pp. 601-629
Author(s):  
Seung-Hwa Rho ◽  
Timothy J. Vogelsang
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Regression Model ◽  
Critical Values ◽  
Missing Observations ◽  
Test Statistics ◽  
Time Series Regression ◽  
Bootstrap Methods ◽  
Time Periods ◽  
Equal Space

In this article, we investigate the properties of heteroskedasticity and autocorrelation robust (HAR) test statistics in time series regression settings when observations are missing. We primarily focus on the nonrandom missing process case where we treat the missing locations to be fixed asT→ ∞ by mapping the missing and observed cutoff dates into points on [0,1] based on the proportion of time periods in the sample that occur up to those cutoff dates. We consider two models, the amplitude modulated series (Parzen, 1963) regression model, which amounts to plugging in zeros for missing observations, and the equal space regression model, which simply ignores the missing observations. When the amplitude modulated series regression model is used, the fixed-blimits of the HAR test statistics depend on the locations of missing observations but are otherwise pivotal. When the equal space regression model is used, the fixed-blimits of the HAR test statistics have the standard fixed-blimits as in Kiefer and Vogelsang (2005). We discuss methods for obtaining fixed-bcritical values with a focus on bootstrap methods and find the naivei.i.d.bootstrap with missing dates fixed to be an effective and practical way to obtain the fixed-bcritical values.

LEARNING DYNAMICS AND NONLINEAR MISSPECIFICATION IN AN ARTIFICIAL FINANCIAL MARKET

2009 ◽  
Vol 13 (5) ◽  
pp. 625-655 ◽  
Author(s):  
Christophre Georges ◽  
John C. Wallace
Keyword(s):  
Time Series ◽  
Financial Market ◽  
Consistency Condition ◽  
Nonlinear Structure ◽  
State Variable ◽  
Bounded Memory ◽  
Long Run ◽  
Finite Memory ◽  
Aggregate Dynamics ◽  
True Structure

In this paper, we explore the consequence of learning to forecast in a very simple environment. Agents have bounded memory and incorrectly believe that there is nonlinear structure underlying the aggregate time series dynamics. Under social learning with finite memory, agents may be unable to learn the true structure of the economy and rather may chase spurious trends, destabilizing the actual aggregate dynamics. We explore the degree to which agents' forecasts are drawn toward a minimal state variable learning equilibrium as well as a weaker long-run consistency condition.

scholarly journals Time series regression studies in environmental epidemiology

2013 ◽  
Vol 42 (4) ◽  
pp. 1187-1195 ◽  
Author(s):  
Krishnan Bhaskaran ◽  
Antonio Gasparrini ◽  
Shakoor Hajat ◽  
Liam Smeeth ◽  
Ben Armstrong
Keyword(s):  
Time Series ◽  
Environmental Epidemiology ◽  
Time Series Regression

Forecasting Long-Run Coal Price in China: A Shifting Trend Time-Series Approach

2010 ◽  
Vol 14 (3) ◽  
pp. 499-519 ◽  
Author(s):  
Baomin Dong ◽  
Xuefeng Li ◽  
Boqiang Lin
Keyword(s):  
Time Series ◽  
Coal Price ◽  
Long Run ◽  
Time Series Approach

scholarly journals Relationship between daily suicide counts and temperature in England and Wales

2007 ◽  
Vol 191 (2) ◽  
pp. 106-112 ◽  
Author(s):  
Lisa A. Page ◽  
Shakoor Hajat ◽  
R. Sari Kovats
Keyword(s):  
Time Series ◽  
Seasonal Fluctuation ◽  
Daily Temperature ◽  
Short Term ◽  
Time Series Regression ◽  
England And Wales ◽  
Increased Risk ◽  
Hot Weather ◽  
The Impact ◽  
The Relationship

BackgroundSeasonal fluctuation in suicide has been observed in many populations. High temperature may contribute to this, but the effect of short-term fluctuations in temperature on suicide rates has not been studied.AimsTo assess the relationship between daily temperature and daily suicide counts in England and Wales between 1 January 1993 and 31 December 2003 and to establish whether heatwaves are associated with increased mortality from suicide.MethodTime-series regression analysis was used to explore and quantify the relationship between daily suicide counts and daily temperature. The impact of two heatwaves on suicide was estimated.ResultsNo spring or summer peak in suicide was found. Above 18 °, each 1 ° increase in mean temperature was associated with a 3.8 and 5.0% rise in suicide and violent suicide respectively. Suicide increased by 46.9% during the 1995 heatwave, whereas no change was seen during the 2003 heat wave.ConclusionsThere is increased risk of suicide during hot weather.

The Impact of Terms of Trade on the Export Structure of Manufactured Products in Different Economic Developing Status

2021 ◽  
Vol 1 (1) ◽  
pp. 59-67
Author(s):  
Kai-Ting Huang ◽  
Keyword(s):  
Time Series ◽  
Terms Of Trade ◽  
Development Status ◽  
Structural Time Series ◽  
Export Structure ◽  
Primary Products ◽  
Long Run ◽  
Deterministic Trend ◽  
Manufactured Products ◽  
The Impact

The Prebisch-Singer Hypothesis states that in structural time series analysis, the terms of trade between primary products and manufacturers have a negative deterministic trend. Many researchers argued that the deterioration in trade is the type of country in which the products are exported, regardless of whether the types of products exported by such countries are primary or manufactured products. This paper employs a development-differentiated model to analyze the correlation between various terms of trade and the export proportion of manufactured products on different economies of development status. In the long run, stable co-integration relations exist between terms of trade and the export proportion of manufactured products for development status. Furthermore, the increased proportion of manufactured products exports is the Granger casualty for the worse terms of trade for several economies of development status. The results demonstrated that changing the terms of trade is significantly influenced by structured changes in the export proportion of manufactured products for the development status of economies.

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