Unobserved Components Time Series Models Research Articles

Unobserved components with stochastic volatility: Simulation‐based estimation and signal extraction

SummaryThe unobserved components time series model with stochastic volatility has gained much interest in econometrics, especially for the purpose of modelling and forecasting inflation. We present a feasible simulated maximum likelihood method for parameter estimation from a classical perspective. The method can also be used for evaluating the marginal likelihood function in a Bayesian analysis. We show that our simulation‐based method is computationally feasible, for both univariate and multivariate models. We assess the performance of the method in a Monte Carlo study. In an empirical study, we analyse U.S. headline inflation using different univariate and multivariate model specifications.

Inflation, inflation expectations and central bank communication in emerging markets

ABSTRACT The paper studies inflation, inflation expectations, and central bank communication in emerging markets from Africa, Asia and Latin America. The analysis shows that superior central bank communication is associated with greater accuracy in the econometric modelling of inflation and inflation expectations using a benchmark univariate unobserved components time series model. The investigation explores the wider applicability of its approach by examining the United States, Norway, the United Kingdom and Switzerland.

Measuring business cycles: Empirical evidence based on an unobserved component approach

We adopt an unobserved components time series model to track the business cycles in the G7 countries using the Industrial production index over the period from 1:1961 to 8:2017. The advantage of ad...

Unobserved Components with Stochastic Volatility in U.S. Inflation: Estimation and Signal Extraction

We consider unobserved components time series models where the components are stochastically evolving over time and are subject to stochastic volatility. It enables the disentanglement of dynamic structures in both the mean and the variance of the observed time series. We develop a simulated maximum likelihood estimation method based on importance sampling and assess its performance in a Monte Carlo study. This modelling framework with trend, seasonal and irregular components is applied to quarterly and monthly US inflation in an empirical study. We find that the persistence of quarterly inflation has increased during the 2008 financial crisis while it has recently returned to its pre-crisis level. The extracted volatility pattern for the trend component can be associated with the energy shocks in the 1970s while that for the irregular component responds to the monetary regime changes from the 1980s. The scale of the changes in the seasonal component has been largest during the beginning of the 1990s. We finally present empirical evidence of relative improvements in the accuracies of point and density forecasts for monthly US inflation.

Structural Intervention Time Series Analysis of Crime Rates: The Impact of Sentence Reform in Virginia

AbstractWe adopt a structural time series analysis to investigate the impact of parole abolitionand sentence reform in Virginia on reported crime rates. The Commonwealth of Virginiaabolished parole and reformed sentencing for all felony offences committed on or afterJanuary 1, 1995. To examine the impact of Virginia’s change in legislation on reportedcrime rates from 1995 onwards, we perform an intervention time series analysis basedon structural time series models. We empirically find that the change in legislation hassignificantly reduced the burglary rates and to a lesser extent the murder rates in Virginia.For other violent crimes such as rape and aggravated assault the evidence of a significantreduction in crime rates is less evident or is not found. This empirical study for Virginiaalso provides an illustration of how an effective intervention time series analysis can becarried out in crime studies.Keywords: Intervention time series analysis; Crime rates; Structural time series models;Unobserved components time series models.

The Effect of the Great Moderation on the U.S. Business Cycle in a Time-Varying Multivariate Trend-Cycle Model

In this paper we investigate whether the dynamic properties of the U.S. business cycle have changed in the last fifty years. For this purpose we develop a flexible business cycle indicator that is constructed from a moderate set of macroeconomic time series. The coincident economic indicator is based on a multivariate trend-cycle decomposition model that accounts for time variation in macroeconomic volatility, known as the great moderation. In particular, we consider an unobserved components time series model with a common cycle that is shared across different time series but adjusted for phase shift and amplitude. The extracted cycle can be interpreted as the result of a model-based bandpass filter and is designed to emphasize the business cycle frequencies that are of interest to applied researchers and policymakers. Stochastic volatility processes and mixture distributions for the irregular components and the common cycle disturbances enable us to account for all the heteroskedasticity present in the data. The empirical results are based on a Bayesian analysis and show that time-varying volatility is only present in the a selection of idiosyncratic components while the coefficients driving the dynamic properties of the business cycle indicator have been stable over time in the last fifty years.

Measuring financial cycles in a model-based analysis: Empirical evidence for the United States and the euro area

We adopt an unobserved components time series model to extract financial cycles for the United States and the five largest euro area countries over the period 1970–2014. We find that financial cycles can parsimoniously be estimated by house prices and total credit or the credit-to-GDP ratio. We show that these medium-term cycles are longer and have larger amplitudes than business cycles, and that their length and amplitude vary over time and across countries.

Measuring Financial Cycles in a Model-Based Analysis: Empirical Evidence for the United States and the Euro Area

We adopt an unobserved components time series model to extract financial cycles for the United States and the five largest euro area countries over the period 1970 to 2014. We find that credit, the credit-to-GDP ratio and house prices have medium-term cycles which share a few common statistical properties. We show that financial cycles are longer and more ample than business cycles, and that their length and amplitude vary over time and across countries.

Measuring Financial Cycles with a Model-Based Filter: Empirical Evidence for the United States and the Euro Area

The financial cycle captures systematic patterns in the financial system and is closely related to the concept of procyclicality of systemic risk. This paper investigates the characteristics of financial cycles using a multivariate model-based filter. We extract cycles using an unobserved components time series model and applying state space methods. We estimate financial cycles for the United States, Germany, France, Italy, Spain and the Netherlands, using data from 1970 to 2014. For these countries, we find that the individual financial variables we examine have medium-term cycles which share a few common statistical properties. We therefore refer to these cycles as 'similar'. We find that overall financial cycles are longer than business cycles and have a higher amplitude. Moreover, such behavior varies over time and across countries. Our results suggest that estimates of the financial cycle can be a useful monitoring tool for policymakers as they may provide a broad indication about when risks to financial stability increase, remain stable, or decrease.

Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox

AbstractThis paper details particle Markov chain Monte Carlo (PMCMC) techniques for analysis of unobserved component time series models using several economic data sets. The objective of this paper is to explain the basics of the methodology and provide computational applications that justify applying PMCMC in practice. For instance, we use PMCMC to estimate a stochastic volatility model with a leverage effect, Student-t distributed errors or serial dependence. We also model time series characteristics of monthly US inflation rate by considering a heteroskedastic ARFIMA model where heteroskedasticity is specified by means of a Gaussian stochastic volatility process.

The Trickle‐down Effect of the Mining Boom in Australia: Fact or Myth?

This paper examines the relationship between the output levels in the mining sector and various non‐mining sectors in an attempt to understand the role of the mining sector in Australia. The unobserved components time series model is used to estimate the effects of the output gap and the growth regime in the mining sector on the output level of each of several non‐mining sectors. Overall, the estimates obtained do not suggest an overwhelmingly positive effect running from the mining sector to other production and services sectors, implying that the trickle‐down effect of the mining boom may be a myth.

Particle Gibbs with Ancestor Sampling Methods for Unobserved Component Time Series Models with Heavy Tails, Serial Dependence and Structural Breaks

Particle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox

This paper details particle Markov chain Monte Carlo (PMCMC) techniques for analysis of unobserved component time series models using several economic data sets. The objective of this paper is to explain the basics of the methodology and provide computational applications that justify applying PMCMC in practice. For instance, we use PMCMC to estimate a stochastic volatility model with a leverage effect, Student-t distributed errors or serial dependence. We also model time series characteristics of monthly US inflation rate by considering a heteroskedastic ARFIMA model where heteroskedasticity is specified by means of a Gaussian stochastic volatility process.

Forecasting macroeconomic variables using collapsed dynamic factor analysis

We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence of the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a US macroeconomic dataset. The unbalanced panel contains quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher levels of forecasting precision when the panel size and time series dimensions are moderate.

Economic Trends and Cycles in Crime: A Study for England and Wales

Summary This paper models cyclical behaviour in property crime series (burglary and theft) in relation to the macroeconomic activity indicators in England and Wales in the period from 1955 to 2001. Using unobserved components (UC) time series models, univariate time series analysis suggests that recorded burglary (theft) data is subject to stochastic cycle processes with typical business cycle frequencies of approximately 5 and 10 years. In the multivariate UC time series framework, recorded burglary (theft) is simultaneously modelled in a trivariate model, together with unemployment and real GDP time series. We also estimate a five-variate model, where we simultaneously model burglary, theft, unemployment, real GDP, and police variables. Some interesting findings in these analyses are: (i) observed cyclical behaviour in recorded property crime is almost fully determined by the economic business cycles; (ii) explanatory variables such as sentence length, imprisonment and conviction rates affect the short-term dynamics more than the long-term dynamics; (iii) motivational and opportunity effects between macroeconomic and crime time series can be distinguished in our modelling framework.

Forecasting Macroeconomic Variables Using Collapsed Dynamic Factor Analysis

We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence for the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a U.S. macroeconomic dataset. The unbalanced panel contain quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher forecasting precisions when panel size and time series dimensions are moderate.

Extracting a robust US business cycle using a time‐varying multivariate model‐based bandpass filter

AbstractWe develop a flexible business cycle indicator that accounts for potential time variation in macroeconomic variables. The coincident economic indicator is based on a multivariate trend cycle decomposition model and is constructed from a moderate set of US macroeconomic time series. In particular, we consider an unobserved components time series model with a common cycle that is shared across different time series but adjusted for phase shift and amplitude. The extracted cycle can be interpreted as a model‐based bandpass filter and is designed to emphasize the business cycle frequencies that are of interest to applied researchers and policymakers. Stochastic volatility processes and mixture distributions for the irregular components and the common cycle disturbances enable us to account for the heteroskedasticity present in the data. Forecasting results are presented for a set of different specifications. Point forecasts from the preferred model indicate a future recession with the uncertainty over the business cycle growing quickly as the forecast horizon increases. Copyright © 2010 John Wiley & Sons, Ltd.

Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment

We introduce a general class of periodic unobserved component (UC) time series models with stochastic trend and seasonal components and with a novel periodic stochastic cycle component. The general state space formulation of the periodic model allows for exact maximum likelihood estimation, signal extraction and forecasting. The consequences for model-based seasonal adjustment are discussed. The new periodic model is applied to postwar monthly US unemployment series from which we identify a significant periodic stochastic cycle. A detailed periodic analysis is presented including a comparison between the performances of periodic and non-periodic UC models.

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

SummaryUnobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, which is often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear–additive framework may be too restrictive. We formulate a non-linear unobserved components time series model which allows interactions between the trend–cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle-dependent seasonal fluctuations.

Seasonality with Trend and Cycle Interactions in Unobserved Components Models

Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance, and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. In this paper, we formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle dependent seasonal fluctuations.