Irma Hindrayanto

Exact maximum likelihood estimation for non-stationary periodic time series models

Time series models with parameter values that depend on the seasonal index are commonly referred to as periodic models. Periodic formulations for two classes of time series models are considered: seasonal autoregressive integrated moving average and unobserved components models. Convenient state space representations of the periodic models are proposed to facilitate model identification, specification and exact maximum likelihood estimation of the periodic parameters. These formulations do not require a priori (seasonal) differencing of the time series. The time-varying state space representation is an attractive alternative to the time-invariant vector representation of periodic models which typically leads to a high dimensional state vector in monthly periodic time series models. A key development is our method for computing the variance-covariance matrix of the initial set of observations which is required for exact maximum likelihood estimation. The two classes of periodic models are illustrated for a monthly postwar US unemployment time series.

Nowcasting and forecasting economic growth in the euro area using principal components

Many empirical studies have shown that factor models produce relatively accurate forecasts compared to alternative short-term forecasting models. These empirical findings have been established for different macroeconomic data sets and different forecast horizons. However, various specifications of the factor model exist and it is a topic of debate which specification is most effective in its forecasting performance. Furthermore, the forecast performances of the different specifications during the recent financial crisis are also not well documented. In this study we investigate these two issues in depth. We empirically verify the forecast performance of three factor model approaches and report our findings in an extended empirical out-of-sample forecasting competition for quarterly growth of gross domestic product in the euro area and its five largest countries over the period 1992-2012. We also introduce two extensions of existing factor models to make them more suitable for real-time forecasting. We show that the factor models have been able to systematically beat the benchmark autoregressive model, both before as well as during the financial crisis. The recently proposed collapsed dynamic factor model shows the highest forecast accuracy for the euro area and the majority of countries that we have analyzed. The forecast precision improvements against the benchmark model can range up to 77% in mean square error reduction, depending on the country and forecast horizon.

Modeling trigonometric seasonal components for monthly economic time series

The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this article, we explore a generalization of the basic structural time series model in which the time-varying trigonometric terms associated with different seasonal frequencies have different variances for their disturbances. The contribution of the article is two-fold. The first aim is to investigate the dynamic properties of this frequency-specific Basic Structural Model (BSM). The second aim is to relate the model to a comparable generalized version of the Airline model developed at the US Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalized models have properties that are close to each other compared to their default counterparts. In some settings, the distance between the models is almost zero so that the models can be regarded as observationally equivalent. An extensive empirical study on disaggregated monthly shipment and foreign trade series illustrates the improvements of the frequency-specific extension and investigates the relations between the two classes of models.

Trend-Cycle-Seasonal Interactions: Identification and Estimation

Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits non-zero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

On Trend-Cycle-Seasonal Interactions

Traditional unobserved component models assume that the trend, cycle and seasonal components of an individual time series evolve separately over time. Although this assumption has been relaxed in recent papers that focus on trend-cycle interactions, it remains at the core of all seasonal adjustment methods applied by official statistical agencies around the world. The present paper develops an unobserved components model that permits non-zero correlations between seasonal and non-seasonal shocks, hence allowing testing of the uncorrelated assumption that is traditionally imposed. Identification conditions for estimation of the parameters are discussed, while applications to observed time series illustrate the model and its implications for seasonal adjustment.