ASYMPTOTIC PROPERTIES OF THE CUSUM ESTIMATOR FOR THE TIME OF CHANGE IN LINEAR PANEL DATA MODELS

2016 ◽  
Vol 33 (2) ◽  
pp. 366-412 ◽  
Author(s):  
Lajos Horváth ◽  
Marie Hušková ◽  
Gregory Rice ◽  
Jia Wang
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Common Factor ◽  
Asymptotic Properties ◽  
Real Data ◽  
Stationary Time Series ◽  
Model Errors ◽  
Cross Sectional ◽  
Monte Carlo Simulation Study ◽  
The Common

We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the cross-sectional units in the form of a common factor. A CUSUM type estimator is proposed, and we establish first and second order asymptotics that can be used to derive consistent confidence intervals for the time of change. Our results improve upon existing theory in two primary directions. Firstly, the conditions we impose on the model errors only pertain to the order of their long run moments, and hence our results hold for nearly all stationary time series models of interest, including nonlinear time series like the ARCH and GARCH processes. Secondly, we study how the asymptotic distribution and norming sequences of the estimator depend on the magnitude of the changes in each cross-section and the common factor loadings. The performance of our results in finite samples is demonstrated with a Monte Carlo simulation study, and we consider applications to two real data sets: the exchange rates of 23 currencies with respect to the US dollar, and the GDP per capita in 113 countries.

Detecting common breaks in the means of high dimensional cross-dependent panels

2021 ◽  
Author(s):  
Lajos Horváth ◽  
Zhenya Liu ◽  
Gregory Rice ◽  
Yuqian Zhao
Keyword(s):  
Panel Data ◽  
Common Factors ◽  
Real Data ◽  
Change Points ◽  
High Dimensional ◽  
Asymptotic Results ◽  
Cross Sectional ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Cross Sectional Dependence

Abstract The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross–sectional dependence is considered. Under the assumption that the cross–sectional dependence is captured by an unknown number of common factors, a new CUSUM type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross sectional time series of length T, the asymptotic results hold under the mild assumption that min {N, T} → ∞, with an otherwise arbitrary relationship between N and T, allowing the results to apply to most panel data examples. Bootstrap procedures are proposed to approximate the sampling distribution of the test statistics. A Monte Carlo simulation study showed that our test outperforms several other existing tests in finite samples in a number of cases, particularly when N is much larger than T. The practical application of the proposed results are demonstrated with real data applications to detecting and estimating change points in the high dimensional FRED-MD macroeconomic data set.

An easy way to create duration variables in binary cross-sectional time-series data

2020 ◽  
Vol 20 (4) ◽  
pp. 916-930
Author(s):  
Andrew Q. Philips
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Time Series Data ◽  
Series Data ◽  
Duration Dependence ◽  
Cross Sectional ◽  
Common Solution ◽  
The Common

In cross-sectional time-series data with a dichotomous dependent variable, failing to account for duration dependence when it exists can lead to faulty inferences. A common solution is to include duration dummies, polynomials, or splines to proxy for duration dependence. Because creating these is not easy for the common practitioner, I introduce a new command, mkduration, that is a straightforward way to generate a duration variable for binary cross-sectional time-series data in Stata. mkduration can handle various forms of missing data and allows the duration variable to easily be turned into common parametric and nonparametric approximations.

scholarly journals Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property

2021 ◽  
Vol 5 (1) ◽  
pp. 19
Author(s):  
Alexander Kushnir ◽  
Alexander Varypaev
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Multivariate Time Series ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Stationary Time Series ◽  
Strong Mixing ◽  
Statistical Estimates ◽  
Distribution Parameters ◽  
M Estimates

The publication is devoted to studying asymptotic properties of statistical estimates of the distribution parameters u∈Rq of a multidimensional random stationary time series zt∈Rm, t∈ℤ satisfying the strong mixing conditions. We consider estimates u^nδ(z¯n), z¯n=(z1T,…,znT)T∈Rmn that provide in asymptotic n→∞ the maximum values for some objective functions Qn(z¯n;u), which have properties similar to the well-known property of local asymptotic normality. These estimates are constructed by solving the equations δn(z¯n;u)=0, where δn(z¯n;u) are arbitrary functions for which δn(z¯n;u)−gradhQn(z¯n;u+n−1/2h)→0(n→∞) in Pn,u(z¯n)-probability uniformly on u∈U, were U is compact in Rq. In many cases, the estimates u^nδ(z¯n) have the same asymptotic properties as well-known M-estimates defined by equations u^nQ(z¯n)=arg maxu∈UQn(z¯n;u) but often can be much simpler computationally. We consider an algorithmic method for constructing estimates u^nδ(z¯n), which is similar to the accumulation method first proposed by R. Fischer and rigorously developed by L. Le Cam. The main theoretical result of the article is the proof of the theorem, in which conditions of the asymptotic normality of estimates u^nδ(z¯n) are formulated, and the expression is proposed for their matrix of asymptotic mean-square deviations limn→∞nEn,u{(u^δ(z¯n)−u)(u^δ(z¯n)−u)T}.

scholarly journals The Effect of Foreign Portfolio Equity Purchases on Security Returns in Kenya: Evidence from NSE Listed Financial Institutions

2017 ◽  
Vol 9 (4) ◽  
pp. 202
Author(s):  
Loice Koskei
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Stock Returns ◽  
Financial Institutions ◽  
Sampling Technique ◽  
Ordinary Least Squares ◽  
Capital Requirements ◽  
Cross Sectional ◽  
International Portfolio ◽  
Security Returns

Foreign portfolio inflows increase the liquidity and the volume of finance available for financial institutions. At the same time, as foreign portfolio inflows finances in part the capital requirements of local companies, it can also increase the competitiveness of these companies. A huge surge of the inflows can be very inflationary because this forces the Central Bank of Kenya to expand the country’s monetary base by releasing counterpart domestic currency which eventually feeds into the inflationary process. The main aim of this study was to find out the effect of international portfolio equity purchases on security returns of listed financial institutions in Kenya. The study population was 21 financial institutions listed on the Nairobi Securities Exchange. Using purposive sampling technique the study concentrated on 14 financial institutions. The research design of the study was causal as it is concerned more with understanding the connection between cause and effect relationships. The study adopted panel data regression using the Ordinary Least Squares (OLS) method where the data included time series and cross-sectional. A unit root test was carried in this study to examine stationarity of variables because it used panel data which combined both cross-sectional and time series information. Panel estimation results indicated that international portfolio equity purchases have no effect on stock returns of listed financial institutions in Kenya. The study recommended implementation of regulations and policies that would attract foreign portfolio equity inflows in financial institutions.

scholarly journals Presence and Sources of Contrarian Profits in the Bangladesh Stock Market

2018 ◽  
Vol 20 (1) ◽  
pp. 84-104
Author(s):  
Shah Saeed Hassan Chowdhury ◽  
Rashida Sharmin ◽  
M Arifur Rahman
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Stock Returns ◽  
Common Factor ◽  
Relative Strength ◽  
Specific Information ◽  
Cross Sectional ◽  
Market Sentiment ◽  
Holding Period ◽  
Momentum Profits

This article, using weekly data for the period 2002 through 2013, investigates the presence of both contrarian and momentum profits and their sources in the Bangladesh stock market. It follows the methodology of Lo and MacKinlay ( Review of Financial Studies, 1990, 3(2), 175–205) to form portfolios with a weighted relative strength scheme (WRSS). The methodology of Jegadeesh and Titman ( Review of Financial Studies, 1995, 8(4), 973–993) is used to decompose the contrarian/momentum profits into three elements: compensation for cross-sectional risk, lead–lag effect in time series with respect to the common factor and the time-series pattern of stock returns. Results provide the evidence of significant contrarian profits for the holding period of one through eight weeks. There is a stronger presence of contrarian profits during 2002–2008 sub-period. The time-series pattern is found to be the main source of contrarian profits, suggesting that idiosyncratic (firm-specific) information is the main contributor to contrarian profits. Interestingly, the influence of idiosyncratic information on such profits has gradually decreased since 2008. Contrarian profits are robust to market sentiment and other systematic risk factors.

scholarly journals The Effect of Foreign Portfolio Equity Sales on Stock Returns in Kenya: Evidence from NSE Listed Financial Institutions

2017 ◽  
Vol 9 (4) ◽  
pp. 185
Author(s):  
Loice Koskei
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Stock Returns ◽  
Financial Institutions ◽  
Unit Root Test ◽  
Sampling Technique ◽  
Ordinary Least Squares ◽  
Cross Sectional ◽  
High Volatility ◽  
Study Population

Fluctuations of foreign portfolio equity intensify risk and unpredictability in financial institutions leading to high volatility. The main aim of this study was to find out the effect of foreign portfolio equity outflows on stock returns of listed financial institutions in Kenya. The study population was 21 financial institutions listed on the Nairobi Securities Exchange. Using purposive sampling technique the study concentrated on 14 financial institutions. The research design of the study was causal as it is concerned more with understanding the connection between cause and effect relationships. The study adopted panel data regression using the Ordinary Least Squares (OLS) method where the data included time series and cross-sectional. A unit root test was carried in this study to examine stationarity of variables because it used panel data which combined both cross-sectional and time series information. Panel estimation results indicated that foreign portfolio equity outflows have no effect on stock returns of listed financial institutions in Kenya. The study recommended implementation of policies that would curb foreign portfolio outflows in financial institutions in order to minimize reversals of foreign portfolio investments. 

scholarly journals Forecasting using cross-section average–augmented time series regressions

2020 ◽  
Author(s):  
Hande Karabiyik ◽  
Joakim Westerlund
Keyword(s):  
Time Series ◽  
Cross Section ◽  
Regression Models ◽  
Common Factor ◽  
Principal Component ◽  
Small Sample ◽  
Interactive Effects ◽  
Cross Sectional ◽  
Second Development ◽  
The Cross

Summary There is a large and growing body of literature concerned with forecasting time series variables by the use of factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is then estimated, conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared with estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the cross-sectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average–augmented regressions. In contrast to most existing studies, the investigation is carried out while allowing the number of factors to be unknown.

Anomalies and False Rejections

2020 ◽  
Vol 33 (5) ◽  
pp. 2134-2179 ◽  
Author(s):  
Tarun Chordia ◽  
Amit Goyal ◽  
Alessio Saretto
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Real Data ◽  
Multiple Hypothesis Testing ◽  
Statistical Properties ◽  
Trading Strategies ◽  
Cross Sectional ◽  
Publication Process ◽  
Multiple Hypothesis ◽  
Expected Proportion

Abstract We use information from over 2 million trading strategies randomly generated using real data and from strategies that survive the publication process to infer the statistical properties of the set of strategies that could have been studied by researchers. Using this set, we compute $t$-statistic thresholds that control for multiple hypothesis testing, when searching for anomalies, at 3.8 and 3.4 for time-series and cross-sectional regressions, respectively. We estimate the expected proportion of false rejections that researchers would produce if they failed to account for multiple hypothesis testing to be about 45%.

scholarly journals ASYMPTOTICALLY UNBIASED ESTIMATION OF AUTOCOVARIANCES AND AUTOCORRELATIONS WITH LONG PANEL DATA

2010 ◽  
Vol 26 (5) ◽  
pp. 1263-1304 ◽  
Author(s):  
Ryo Okui
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Unobserved Heterogeneity ◽  
Small Samples ◽  
Unbiased Estimation ◽  
Series Length ◽  
Cross Sectional ◽  
Long Run ◽  
The Individual ◽  
Time Invariant

An important reason for analyzing panel data is to observe the dynamic nature of an economic variable separately from its time-invariant unobserved heterogeneity. This paper examines how to estimate the autocovariances of a variable separately from its time-invariant unobserved heterogeneity. When both cross-sectional and time series sample sizes tend to infinity, we show that the within-group autocovariances are consistent, although they are severely biased when the time series length is short. The biases have the leading term that converges to the long-run variance of the individual dynamics. This paper develops methods to estimate the long-run variance in panel data settings and to alleviate the biases of the within-group autocovariances based on the proposed long-run variance estimators. Monte Carlo simulations reveal that the procedures developed in this paper effectively reduce the biases of the estimators for small samples.

Asymptotic properties of certain functionals of the periodogram

1974 ◽  
Vol 11 (3) ◽  
pp. 578-581
Author(s):  
Herbert T. Davis
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Asymptotic Properties ◽  
Innovation Process ◽  
Triangular Array ◽  
Stationary Time Series ◽  
Riemann Sums ◽  
Stationary Time ◽  
Fundamental Frequencies

The asymptotic properties of the periodogram of a weakly stationary time series for the triangular array of fundamental frequencies is studied. For linear Gaussian processes, results are obtained relating the asymptotic distribution of certain Riemann sums of the periodogram of the process to those of the periodogram of the innovation process.

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