Vector Autoregressive Time Series Model Research Articles

Diagnostic checking of periodic vector autoregressive time series models with dependent errors

In this article, we study the asymptotic behaviour of the residual autocorrelations for periodic vector autoregressive time series models (PVAR henceforth) with uncorrelated but dependent innovations (i.e., weak PVAR). We then deduce the asymptotic distribution of the Ljung–Box-McLeod modified Portmanteau statistics for weak PVAR models. In Monte Carlo experiments, we illustrate that the proposed test statistics have reasonable finite sample performance. When the innovations exhibit conditional heteroscedasticity or other forms of dependence, it appears that the standard test statistics (under independent and identically distributed innovations) are generally unreliable, overrejecting, or underrejecting severely, while the proposed test statistics offer satisfactory levels. The proposed methodology is employed in the analysis of two river flows.

The transmission of monetary policy shocks through the markets for reserves and money

This paper identifies supply and demand curves for bank reserves and a Divisia aggregate of monetary services within a structural vector autoregressive time-series model. Estimated over four sample periods spanning 1967 through 2020, the model illustrates how monetary policy actions can be interpreted with reference to their initial impact on bank reserves and the federal funds rate and their subsequent effects on Divisia money, nominal consumption spending, the aggregate nominal price level, and the unemployment rate. Model estimates attribute strong inflationary effects to monetary policy in the late 1960s and 1970s and also show that changes in the supply of reserves associated with the Fed's large-scale asset purchases since 2008 worked, as intended, to offset deflationary pressures and reduce unemployment. The model describes a much richer monetary policy process than one focused on interest rates alone.

Margin‐closed vector autoregressive time series models

Conditions are obtained for a Gaussian vector autoregressive time series of order , VAR(), to have univariate margins that are autoregressive of order or lower‐dimensional margins that are also VAR(). This can lead to ‐dimensional VAR() models that are closed with respect to a given partition of by specifying marginal serial dependence and some cross‐sectional dependence parameters. The special closure property allows one to fit the subprocesses of multi‐variate time series before assembling them by fitting the dependence structure between the subprocesses. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR() process with non‐Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher‐dimensional time series and a multi‐stage estimation procedure can be used. The proposed class of models is applied to a macro‐economic data set and compared with the relevant benchmark models.

Least absolute deviations estimation for nonstationary vector autoregressive time series models with pure unit roots

Least absolute deviations estimation for nonstationary vector autoregressive time series models with pure unit roots

Modelling and forecasting of new cases, deaths and recover cases of COVID-19 by using Vector Autoregressive model in Pakistan.

COVID-19 emerged in Wuhan, China in December 2019 has now spread around the world causes damage to human life and economy. Pakistan is also severely effected by COVID-19 with 202,955 confirmed cases and total deaths of 4,118. Vector Autoregressive time series models was used to forecast new daily confirmed cases, deaths and recover cases for ten days. Our forecasted model results show maximum of 5,363/day new cases with 95% confidence interval of 3,013-8,385 on 3rd of July, 167/day deaths with 95% confidence interval of 112-233 and maximum recoveries 4,016/day with 95% confidence interval of 2,182-6,405 in the next 10 days. The findings of this research may help government and other agencies to reshape their strategies according to the forecasted situation. As the data generating process is identified in terms of time series models, then it can be updated with the arrival of new data and provide forecasted scenario in future.

Social media and depression symptoms: A network perspective.

Passive social media use (PSMU)-for example, scrolling through social media news feeds-has been associated with depression symptoms. It is unclear, however, if PSMU causes depression symptoms or vice versa. In this study, 125 students reported PSMU, depression symptoms, and stress 7 times daily for 14 days. We used multilevel vector autoregressive time-series models to estimate (a) contemporaneous, (b) temporal, and (c) between-subjects associations among these variables. (a) More time spent on PSMU was associated with higher levels of interest loss, concentration problems, fatigue, and loneliness. (b) Fatigue and loneliness predicted PSMU across time, but PSMU predicted neither depression symptoms nor stress. (c) Mean PSMU levels were positively correlated with several depression symptoms (e.g., depressed mood and feeling inferior), but these associations disappeared when controlling for all other variables. Altogether, we identified complex relations between PSMU and specific depression symptoms that warrant further research into potentially causal relationships. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Measuring the Dynamic Predictive Relationship of Social Media Metrics with Firm Equity Value: A Time Series Analysis

In the online environment, social media metrics offer a credible basis of customer feedback in anticipating the firm performance. This study verifies the association of social media metrics of Face-book and Twitter to financial market performance. Data were collected from official Facebook pages and Twitter accounts of 3 fast-food companies over the time period of 6 months. Then established multiple metrics for respective social media platforms and develop outcomes using Vector Autoregressive time series models to evaluate the instantaneous and continuing relationship between social media metrics and financial market performance of the firms in terms of unusual returns and idiosyncratic risk. Results indicated that FB metrics are significant leading indicators of firm equity value. However, Twitter metrics, have a weaker relationship with firm value as compared to FB metrics. Collectively, current research extends new visions for organizational top executives and investors concerning organizational equity valuation and the social media power transformation.

Online interest regarding violent attacks, gun control, and gun purchase: A causal analysis.

BackgroundIncreased interest about gun ownership and gun control are oftentimes driven by informational shocks in a common factor, namely violent attacks, and the perceived need for higher levels of safety. A causal depiction of the societal interest around violent attacks, gun control and gun purchase, both synchronous and over time, should be a stepping stone for designing future strategies regarding the safety concerns of the U.S. population.ObjectiveExamine the causal relationships between unexpected increases in population interest about violent attacks, gun control, and gun purchase.MethodsRelationships among online searches for information about violent attacks, gun control, and gun purchase occurring between 2004 and 2017 in the U.S. are explained through a novel structural vector autoregressive time series model to account for simultaneous causal relationships.ResultsMore than 20% of the stationary variability in each of gun control and gun purchase interest can be explained by the remaining factors. Gun control interest appears to be caused, in part, by violent attacks informational shocks, yet violent attacks, although impactful, have a lesser effect than gun control debate on long-term gun ownership interests.ConclusionsThe form in which gun control has been introduced in public debate may have further increased gun ownership interest. Reactive gun purchase interest may be an unintended side effect of gun control debate. U.S. policymakers may need to rethink current approaches to promotion of gun control, and whether societal policy debate without policy outcomes could be having unintended effects.

Forecasting prices of coffee seeds using Vector Autoregressive Time Series Model

Forecasts of agricultural prices are useful to the farmers, policymakers and agribusiness industries. In this globalized world, management of food security in the developing countries like India where agriculture is dominated needs efficient and reliable price forecasting models. In the present study, Vector Autoregression (VAR) has been applied for modeling and forecasting of monthly wholesale price of clean coffee seeds in different coffee consuming centers, viz. Bengaluru, Chennai and Hyderabad. Augmented Dickey-Fuller (ADF) test has been used for testing the stationarity of the time series. The appropriate VAR model is selected based on minimum Akaike Information Criterion (AIC). The VAR model obtained is compared with the Auto Regressive Integrated Moving Average (ARIMA) models with respect to forecast accuracy measures. The residuals of the fitted models were diagnosed for possible presence of autocorrelation and Autoregressive Conditional Heteroscedasticity (ARCH) effects.

Mecanismos de transmissão de preços entre os mercados doméstico e externo: uma análise sobre as exportações brasileiras de manga entre 2003 e 2013.

Brazil’s São Francisco River Valley, over the years, has emerged as Brazil’s main fruit-producing region, especially noted for mangoes and grapes. The mango produced in this region has reached a good global market position, particularly in Europe and the US. However, increasing domestic price fluctuations on the international market has affected the production and marketing expectations of farmers. The objective of the study is to conduct a price transmission analysis comparing mango export prices with those in the US and European Union markets in the period 2003 to 2013. To that end, a vector autoregressive time series model was estimated to investigate price transmission and impact mechanisms using the impulse-response function. The data used was obtained from Brazil’s Ministry of Development and Foreign Trade and the Food and Agriculture Organization of the United Nations. Among the results, it was found that the Brazilian domestic prices are influenced by the US market prices, and that price shocks in the US market can impact the growth of domestic prices for several months.

Distributions for residual autocovariances in parsimonious periodic vector autoregressive models with applications

The asymptotic distribution of the residual autocovariance matrices in the class of periodic vector autoregressive time series models with structured parameterization is derived. Diagnostic checking with portmanteau test statistics represents a useful application of the result. Under the assumption that the periodic white noise process of the periodic vector autoregressive time series model is composed of independent random variables, we demonstrate that the finite sample distributions of the Hosking‐Li‐McLeod portmanteau test statistics can be approximated by those of weighted sums of independent chi‐square random variables. The quantiles of the asymptotic distribution can be computed using the Imhof algorithm or other exact methods. Thus, using the (single) chi‐square distribution for these test statistics appears inadequate in general, although it is often recommended in practice for diagnostic methods of that kind. A simulation study provides empirical evidence.

Univariate and Multivariate Autoregressive Time Series Models of Offensive Baseball Performance: 1901-2005

This paper sets out to estimate univariate time series models on a selected set of offensive baseball measures from 1901 to 2005. The measures include homeruns, bases on balls, runs batted in, doubles, and stolen bases. The paper next estimates the trends in these statistics simultaneously using a vector autoregressive time series model. Along the way, tests of assumptions underlying the time-series models are provided. Univariate time series results suggest that simple lag--1 models fit these offensive statistics quite well. The multivariate results show that a simple lag--1 vector autoregressive model also fits quite well. The results of the vector time series model indicate that most statistics are strongly predicted by their prior values. However, certain temporal dependencies among baseball measures are observed, suggesting the importance of examining covariation in baseball data over time.

Granger Causality of Coupled Climate Processes: Ocean Feedback on the North Atlantic Oscillation

Abstract This study uses a Granger causality time series modeling approach to quantitatively diagnose the feedback of daily sea surface temperatures (SSTs) on daily values of the North Atlantic Oscillation (NAO) as simulated by a realistic coupled general circulation model (GCM). Bivariate vector autoregressive time series models are carefully fitted to daily wintertime SST and NAO time series produced by a 50-yr simulation of the Third Hadley Centre Coupled Ocean–Atmosphere GCM (HadCM3). The approach demonstrates that there is a small yet statistically significant feedback of SSTs on the NAO. The SST tripole index is found to provide additional predictive information for the NAO than that available by using only past values of NAO—the SST tripole is Granger causal for the NAO. Careful examination of local SSTs reveals that much of this effect is due to the effect of SSTs in the region of the Gulf Steam, especially south of Cape Hatteras. The effect of SSTs on NAO is responsible for the slower-than-exponential decay in lag-autocorrelations of NAO notable at lags longer than 10 days. The persistence induced in daily NAO by SSTs causes long-term means of NAO to have more variance than expected from averaging NAO noise if there is no feedback of the ocean on the atmosphere. There are greater long-term trends in NAO than can be expected from aggregating just short-term atmospheric noise, and NAO is potentially predictable provided that future SSTs are known. For example, there is about 10%–30% more variance in seasonal wintertime means of NAO and almost 70% more variance in annual means of NAO due to SST effects than one would expect if NAO were a purely atmospheric process.

A method for taking models to the data

This paper develops a method for combining the power of a dynamic, stochastic, general equilibrium model with the flexibility of a vector autoregressive time-series model to obtain a hybrid that can be taken directly to the data. It estimates this hybrid model via maximum likelihood and uses the results to address a number of issues concerning the ability of a prototypical real business cycle model to explain movements in aggregate output and employment in the postwar US economy, the stability of the real business cycle model's structural parameters, and the performance of the hybrid model's out-of-sample forecasts.

The Role of the Automotive Industry in Detroit’s Employment Fluctuations: A Multiple Restriction Regime Approach

Using a vector autoregressive time-series model, I analyze the validity of a multiple restriction regime approach in regional modeling as well as the historical impact of various employment shocks on the Detroit Metropolitan Area economy. For this, the model’s decomposition matrix has two distinct forms that are dependent on the relation of an industry to the automotive industry, the region’s largest manufacturing sector, and the causal restrictions these different regimes place on each version of the model. Results indicate that the use of two different sets of restrictions yields acceptable explanatory power and captures important dynamic characteristics of the data without a substantial increase in computational costs over a single restriction regime approach. Results also indicate that declines in employment in the automotive industry over the past two decades did have a negative effect on the Detroit Metropolitan Area, but not of the immediacy or magnitude popularly believed.

A vector autoregressive model to predict hurricane tracks

The stochastic behaviour of hurricane tracks is expressed by a vector autoregressive time series model. Historical data and correlation analysis were used to identify the model structure of a typical hurricane track. The parameter estimation scheme is based on recursive and iterative algorithms. The recursive approach is used when a small number of points have been collected from a hurricane. On the Other hand, iterative algorithms are used when enough information for optimal estimation is available. The multivariate time series model was used to predict hurricane tracks during the 1990 hurricane season in the North Atlantic ocean. Prediction errors from the vector autoregressive model are compared with errors from the NHC90 model. The NHC90 model performs better than the studied model; however, the vector autoregressive model uses a small amount of information and may help to reduce official forecasting errors.

Where Do Betas Come From? Asset Price Dynamics and the Sources of Systematic Risk

In this article we break assets’ betas with common factors into components attributable to news about future cash flows, real interest rates, and excess returns. To achieve this decomposition, we use a vector autoregressive time-series model and an approximate log-linear present value relation. The betas of industry and size portfolios with the market are largely attributed to changing expected returns. Betas with inflation and industrial production reflect opposing cash flow and expected return effects. We also show how asset pricing theory restricts the expected excess return components of betas.

Where do betas come from? Asset price dynamics and the sources of systematic risk

In this article we break asset's betas with common factors into components attributable to news about future cash flows, real interest rates, and excess returns. To achieve this decomposition, we use a vector autoregressive time-series model and an approximate log-linear present value relation. The betas of industry and size portfolios with the market are largely attributed to changing expected returns. Betas with inflation and industrial production reflect opposing cash flow and expected return effects. We also show how asset pricing theory restricts the expected excess return components of betas.