scholarly journals Testing collinearity of vector time series

2019 ◽  
Vol 22 (2) ◽  
pp. 97-116
Author(s):  
Tucker S McElroy ◽  
Agnieszka Jach
Keyword(s):  
Time Series ◽  
Density Matrix ◽  
Spectral Density ◽  
Time Series Data ◽  
Series Data ◽  
Test Statistics ◽  
Rank Reduction ◽  
Spectral Density Matrix ◽  
Schur Complements ◽  
Vector Time Series

Summary We investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. New asymptotic results for the test statistics are derived under the fixed bandwidth ratio paradigm; they diverge under the alternative, but under the null hypothesis of collinearity the test statistics converge to a non-standard limiting distribution. Subsampling is used to obtain the limiting null quantiles. A simulation study and an empirical illustration for 6-variate time series data are provided.

scholarly journals ESTIMATION OF AUTOREGRESSIVE ROOTS NEAR UNITY USING PANEL DATA

2000 ◽  
Vol 16 (6) ◽  
pp. 927-997 ◽  
Author(s):  
Hyungsik R. Moon ◽  
Peter C.B. Phillips
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Time Series Data ◽  
Initial Conditions ◽  
Series Data ◽  
Test Statistics ◽  
Rate Condition ◽  
Panel Models ◽  
Stochastic Trends ◽  
Efficient Extraction

Time series data are often well modeled by using the device of an autoregressive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric techniques and the lack of a consistent estimator complicates inference. This paper develops procedures for the estimation of a common localizing parameter using panel data. Pooling information across individuals in a panel aids the identification and estimation of the localizing parameter and leads to consistent estimation in simple panel models. However, in the important case of models with concomitant deterministic trends, it is shown that pooled panel estimators of the localizing parameter are asymptotically biased. Some techniques are developed to overcome this difficulty, and consistent estimators of c in the region c < 0 are developed for panel models with deterministic and stochastic trends. A limit distribution theory is also established, and test statistics are constructed for exploring interesting hypotheses, such as the equivalence of local to unity parameters across subgroups of the population. The methods are applied to the empirically important problem of the efficient extraction of deterministic trends. They are also shown to deliver consistent estimates of distancing parameters in nonstationary panel models where the initial conditions are in the distant past. In the development of the asymptotic theory this paper makes use of both sequential and joint limit approaches. An important limitation in the operation of the joint asymptotics that is sometimes needed in our development is the rate condition n/T → 0. So the results in the paper are likely to be most relevant in panels where T is large and n is moderately large.

Spectral Analysis for Bivariate Time Series with Long Memory

1996 ◽  
Vol 12 (5) ◽  
pp. 773-792 ◽  
Author(s):  
J. Hidalgo
Keyword(s):  
Time Series ◽  
Density Matrix ◽  
Spectral Density ◽  
Long Memory ◽  
Limit Theorems ◽  
Stationary Process ◽  
Absolute Summability ◽  
Spectral Density Matrix ◽  
Mixing Coefficients ◽  
Long Memory Processes

This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time series, continue to hold for long memory processes when λ lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.

Testing Increasing Sensitivity of Enrollment at Private Institutions to Tuition and other Costs

1996 ◽  
Vol 40 (1) ◽  
pp. 40-45 ◽  
Author(s):  
Yu Hsing ◽  
Hui S. Chang
Keyword(s):  
Higher Education ◽  
Time Series ◽  
Functional Form ◽  
Time Series Data ◽  
Series Data ◽  
Standard Errors ◽  
Private Institutions ◽  
Test Statistics ◽  
Sample Period ◽  
Income Elasticities

This paper re-examines the demand for higher education at private institutions and tests if in recent years enrollment has become more sensitive to rising tuition and other related costs. Time series data between FY 1964–65 and FY 1990–91 are used as the sample. Major findings are interesting. The general functional form yields coefficients with smaller standard errors and larger value of the test statistics. The logarithmic form can be rejected at the 5% level. Tuition elasticities rose from −0.261 to −0.557 and income elasticities also increased from 0.493 to 1.093 during the sample period. Thus, enrollment has become more sensitive to changes in tuition and other costs. However, part of the loss of enrollment due to tuition increases can be recovered by rising income elasticities.

scholarly journals DYNAMIC MODELING OF TIME SERIES DATA USING BEKK-GARCH MODEL

2020 ◽  
Vol 17 (36) ◽  
pp. 1186-1198
Author(s):  
Mustofa USMAN ◽  
N INDRYANI ◽  
WARSONO A. ◽  
AMANTO WAMILIANA
Keyword(s):  
Time Series ◽  
Granger Causality ◽  
Impulse Response ◽  
Time Series Data ◽  
Granger Causality Test ◽  
Share Price ◽  
Series Data ◽  
P Value ◽  
Test Statistics ◽  
Causality Test

The Vector Autoregressive Moving Average (VARMA) model is one of the models that is often used in modeling multivariate time series data. In time-series data of economics, especially data return, they usually have high fluctuations in some periods, so the return volatility is unstable. In modeling data return of share prices ADRO and ITMG, the behavior of high volatility will be considered. This study aims to find the best model that fits the data return of share price of the energy companies of PT Adaro Energy Tbk (ADRO) and PT Indo Tambangraya Megah Tbk (ITMG), to analyze the behavior of impulse response of the variables data return ADRO and ITMG, to analyze the granger causality test, and to forecast the next 12 periods. Based on the selection of the best model using the criteria of AICC, HQC, AIC, and SBC, it was found that the VARMA (2.2) -GARCH (1.1) model is the best one for the data in this study. The model VARMA(2,2)-GARCH (1,1) is then written as a univariate model. For the univariate ADRO model, the test statistics F = 4,73 and P-value = 0,0084, which indicates the model is very significant; and for the univariate ITMG model, the test statistics is F = 5,82 and P-value 0,0001, which indicates the model is significant. Based on the best model selected, the impulse response, Granger causality test, and forecasting for the next 12 periods are discussed.

Asymptotic Expansions of the Distributions of Statistics Related to the Spectral Density Matrix in Multivariate Time Series and Their Applications

1990 ◽  
Vol 6 (1) ◽  
pp. 75-96 ◽  
Author(s):  
Masanobu Taniguchi ◽  
Koichi Maekawa
Keyword(s):  
Time Series ◽  
Density Matrix ◽  
Spectral Density ◽  
Asymptotic Expansions ◽  
Multivariate Time Series ◽  
Principal Component ◽  
Autoregressive Process ◽  
Reduced Form ◽  
Gaussian Stationary Process ◽  
Spectral Density Matrix

Let {X(t)} be a multivariate Gaussian stationary process with the spectral density matrix f0(ω), where θ is an unknown parameter vector. Using a quasi-maximum likelihood estimator θ̂ of θ, we estimate the spectral density matrix f0(ω) by fθ̂(ω). Then we derive asymptotic expansions of the distributions of functions of fθ̂(ω). Also asymptotic expansions for the distributions of functions of the eigenvalues of fθ̂(ω) are given. These results can be applied to many fundamental statistics in multivariate time series analysis. As an example, we take the reduced form of the cobweb model which is expressed as a two-dimensional vector autoregressive process of order 1 (AR(1) process) and show the asymptotic distribution of θ̂, the estimated coherency, and contribution ratio in the principal component analysis based on θ̂ in the model, up to the second-order terms. Although our general formulas seem very involved, we can show that they are tractable by using REDUCE 3.

scholarly journals Atmospheric Cold Front–Induced Exchange Flows through a Microtidal Multi-Inlet Bay: Analysis Using Multiple Horizontal ADCPs and FVCOM Simulations

2019 ◽  
Vol 36 (3) ◽  
pp. 443-472 ◽  
Author(s):  
Chunyan Li ◽  
Wei Huang ◽  
Brian Milan
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Cold Front ◽  
Ocean Model ◽  
Series Data ◽  
Exchange Flows ◽  
Cold Fronts ◽  
Low Pass ◽  
Strong Winds ◽  
Vector Time Series

AbstractAtmospheric cold fronts provide recurring forcing for circulations and long-term transport in estuaries with microtides. Multiple horizontal ADCPs were used to obtain time series data from three inlets in Barataria Bay. The data cover a period of 51 atmospheric cold fronts between 2013 and 2015. The weather and subtidal ocean response are highly correlated in the “weather band” (3–7 days). The cold front–associated winds produce alternating flows into, out of, and then back into the bay, forming an asymmetric “M” for low-pass filtered flows. Results show that cold front–induced flows are the most important component in this region, and the flows can be predicted based on wind vector time series. Numerical simulations using a validated Finite-Volume Coastal Ocean Model (FVCOM) demonstrate that the wind-driven oscillations within the bay are consistent with the quasi-steady state with little influence of the Coriolis effect for cold front–related wind-driven flows. The four major inlets (from the southwest to the northeast) consistently carry 10%, 57%, 21%, and 12% of the tidal exchange of the bay, respectively. The subtidal exchange rates through them however fluctuate greatly with averages of 18% ± 13%, 35% ± 18%, 31% ± 16%, and 16% ± 9%, respectively. Several modes of exchange flows through the multiple inlets are found, consisting of the all-in and all-out mode (45% occurrence) under strong winds perpendicular to the coastline; the shallow-downwind, deep-upwind mode (41%), particularly during wind-relaxation periods; and the upwind-in and downwind-out mode (13%) under northerly or southerly winds. These modes are discussed with the low-pass filtered model results and verified by a forcing–response joint EOF analysis.

scholarly journals Estimation with Aggregate Shocks

2019 ◽  
Vol 87 (3) ◽  
pp. 1365-1398 ◽  
Author(s):  
Jinyong Hahn ◽  
Guido Kuersteiner ◽  
Maurizio Mazzocco
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Series Data ◽  
Model Parameters ◽  
Test Statistics ◽  
Cross Sectional ◽  
Aggregate Shocks ◽  
Combined Use ◽  
The Cross ◽  
Estimation Of Model Parameters

Abstract Aggregate shocks affect most households’ and firms’ decisions. Using three stylized models, we show that inference based on cross-sectional data alone generally fails to correctly account for decision making of rational agents facing aggregate uncertainty. We propose an econometric framework that overcomes these problems by explicitly parameterizing the agents’ decision problem relative to aggregate shocks. Our framework and examples illustrate that the cross-sectional and time-series aspects of the model are often interdependent. Therefore, estimation of model parameters in the presence of aggregate shocks requires the combined use of cross-sectional and time-series data. We provide easy-to-use formulas for test statistics and confidence intervals that account for the interaction between the cross-sectional and time-series variation. Lastly, we perform Monte Carlo simulations that highlight the properties of the proposed method and the risks of not properly accounting for the presence of aggregate shocks.

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