Model selection criteria and quadratic discrimination in ARMA and SETAR time series models

We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach leads to including a correction term in the criteria which does not modify their large sample performance but can produce significant improvement in the performance of the criteria in small samples. Thus we propose a family of criteria which generalizes the commonly used model selection criteria. These ideas can be extended to self exciting autoregressive models (SETAR) and we generalize the proposed approach for these non linear time series models. A Monte-Carlo study shows that this family improves the finite sample performance of criteria such as AIC, corrected AIC and BIC, for ARMA models, and AIC, corrected AIC, BIC and some cross-validation criteria for SETAR models. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error of prediction improves for the efficient criteria. These results are obtained for both linear ARMA models and SETAR models in which we assume that the threshold and the parameters are unknown

Regional employment forecasts with spatial interdependencies

"The labour-market policy-mix in Germany is increasingly being decided on a regional level. This requires additional knowledge about the regional development which (disaggregated) national forecasts cannot provide. Therefore, we separately forecast employment for the 176 German labour- market districts on a monthly basis. We first compare the prediction accuracy of standard time-series methods: autoregressive integrated moving averages (ARIMA), exponentially weighted moving averages (EWMA) and the structural-components approach (SC) in these small spatial units. Second, we augment the SC model by including autoregressive elements (SCAR) in order to incorporate the influence of former periods of the dependent variable on its current value. Due to the importance of spatial interdependencies in small labour-market units, we further augment the basic SC model by lagged values of neighbouring districts in a spatial dynamic panel (SCSAR). The prediction accuracies of the models are compared using the mean absolute percentage forecast error (MAPFE) for the simulated out-of-sample forecast for 2005. Our results show that the SCSAR is superior to the SCAR and basic SC model. ARIMA and EWMA models perform slightly better than SCSAR in many of the German labour-market districts. This reflects that these two moving-average models can better capture the trend reversal beginning in some regions at the end of 2004. All our models have a high forecast quality with an average MAPFE lower than 2.2 percent." (Author's abstract, IAB-Doku) ((en))regionaler Arbeitsmarkt, Beschäftigungsentwicklung, Prognoseverfahren, Arbeitsmarktprognose - Methode

MODEL SELECTION CRITERIA AND QUADRATIC DISCRIMINATION IN ARMA AND SETAR TIME SERIES MODELS

We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach leads to including a correction term in the criteria which does not modify their large sample performance but can produce significant improvement in the performance of the criteria in small samples. Thus we propose a family of criteria which generalizes the commonly used model selection criteria. These ideas can be extended to self exciting autoregressive models (SETAR) and we generalize the proposed approach for these non linear time series models. A Monte-Carlo study shows that this family improves the finite sample performance of criteria such as AIC, corrected AIC and BIC, for ARMA models, and AIC, corrected AIC, BIC and some cross-validation criteria for SETAR models. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error of prediction improves for the efficient criteria. These results are obtained for both linear ARMA models and SETAR models in which we assume that the threshold and the parameters are unknown.

Regional employment forecasts with spatial interdependencies

"The labour-market policy-mix in Germany is increasingly being decided on a regional level. This requires additional knowledge about the regional development which (disaggregated) national forecasts cannot provide. Therefore, we separately forecast employment for the 176 German labour- market districts on a monthly basis. We first compare the prediction accuracy of standard time-series methods: autoregressive integrated moving averages (ARIMA), exponentially weighted moving averages (EWMA) and the structural-components approach (SC) in these small spatial units. Second, we augment the SC model by including autoregressive elements (SCAR) in order to incorporate the influence of former periods of the dependent variable on its current value. Due to the importance of spatial interdependencies in small labour-market units, we further augment the basic SC model by lagged values of neighbouring districts in a spatial dynamic panel (SCSAR). The prediction accuracies of the models are compared using the mean absolute percentage forecast error (MAPFE) for the simulated out-of-sample forecast for 2005. Our results show that the SCSAR is superior to the SCAR and basic SC model. ARIMA and EWMA models perform slightly better than SCSAR in many of the German labour-market districts. This reflects that these two moving-average models can better capture the trend reversal beginning in some regions at the end of 2004. All our models have a high forecast quality with an average MAPFE lower than 2.2 percent." [authors abstract

Use of SARIMA Models to Assess Data-Poor Fisheries: A Case Study With A Sciaenid Fishery Off Portugal

Research on assessment and monitoring methods has primarily focused on fisheries with long multivariate data sets. Less research exists on methods applicable to data-poor fisheries with univariate data sets with a small sample size. In this study, we examine the capabilities of seasonal autoregressive integrated moving average (SARIMA) models to fit, forecast, and monitor the landings of such data-poor fisheries. We use a European fishery on meagre (Sciaenidae: Argyrosomus regius), where only a short time series of landings was available to model (n=60 months), as our case-study. We show that despite the limited sample size, a SARIMA model could be found that adequately fitted and forecasted the time series of meagre landings (12-month forecasts; mean error: 3.5 tons (t); annual absolute percentage error: 15.4%). We derive model-based prediction intervals and show how they can be used to detect problematic situations in the fishery. Our results indicate that over the course of one year the meagre landings remained within the prediction limits of the model and therefore indicated no need for urgent management intervention. We discuss the information that SARIMA model structure conveys on the meagre life-cycle and fishery, the methodological requirements of SARIMA forecasting of data-poor fisheries landings, and the capabilities SARIMA models present within current efforts to monitor the world\u27s data-poorest resources