Abstract
In this work, a cross-validation procedure is used to identify an appropriate Autoregressive Integrated Moving Average model and an appropriate state space model for a time series. A minimum size for the training set is specified. The procedure is based on one-step forecasts and uses different training sets, each containing one more observation than the previous one. All possible state space models and all ARIMA models where the orders are allowed to range reasonably are fitted considering raw data and log-transformed data with regular differencing (up to second order differences) and, if the time series is seasonal, seasonal differencing (up to first order differences). The value of root mean squared error for each model is calculated averaging the one-step forecasts obtained. The model which has the lowest root mean squared error value and passes the Ljung-Box test using all of the available data with a reasonable significance level is selected among all the ARIMA and state space models considered. The procedure is exemplified in this paper with a case study of retail sales of different categories of women's footwear from a Portuguese retailer, and its accuracy is compared with three reliable forecasting approaches. The results show that our procedure consistently forecasts more accurately than the other approaches and the improvements in the accuracy are significant.

Abstract
Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts.

Abstract
Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail supply chains. For profitable retail businesses, accurate sales forecasting is crucial in organizing and planning purchasing, production, transportation and labor force. Retail sales series belong to a special type of time series that typically contain strong trend and seasonal patterns, presenting challenges in developing effective forecasting models. This paper compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. An approach based on cross-validation is used to identify automatically appropriate state space and ARIMA models. The forecasting performance of these models is also compared by examining the out-of-sample forecasts. The results indicate that the overall out-of-sample forecasting performance of ARIMA models evaluated via RMSE, MAE and MAPE is better than state space models. The performance of both forecasting methodologies in producing forecast intervals was also evaluated and the results indicate that ARIMA produces slightly better coverage probabilities than state space models for the nominal 95% forecast intervals. For the nominal 80% forecast intervals the performance of state space models is slightly better.

Abstract
The progress in medical science and the decline of altruistic behavior of couples introduced to the world the ageing problem. The existence of ageing is more experienced by developed countries. Researchers and policy makers are constantly trying to find ways to study the impacts of ageing since the issue is unprecedented in our history. However, the majority of the literature focus more on immediate mechanisms such as public expenditures and somehow neglected the influence of ageing on manufacturing sector. Thus, through panel data, we studied the influence of ageing on manufacturing sectors. The empirical study was carried out on six developed countries namely Japan, Germany, Italy, Greece, Finland and Portugal that have high ageing population. Our results suggest that the growth of the old age group over 65 years old will have significantly negative influence on percentage contribution of manufacturing to the GDP of these countries. Moreover, the results also demonstrate that a country with a higher proportion of old age group over working group will face fall in the manufacturing.

Abstract
Aggressive marketing causes rapid changes in consumer behavior and some significant impact in the retail business. In this context, the sales forecasting at the SKU level can help retailers to become more competitive by reducing inventory investment and distribution costs. Sales forecasts are often obtained combining basic univariate forecasting models with empirical judgment. However, more effective forecasting methods can be obtained by incorporating promotional information, including price, percentage of discount (direct discount or loyalty card discount), calendar events and weekend indicators not only from the focal product but also from its competitors. To deal with the high dimensionality of the variable space, we propose a two-stage LASSO regression to select optimal predictors and estimate the model parameters. At the first stage, only focal SKUs promotional explanatory variables are included in the Autoregressive Distributed Lag model. At the second stage, the in-sample forecast errors from the first stage are regressed on the explanatory variables from the other SKUs in the same category with the focal SKU, and to use that information more effectively three different approaches were considered: select the five top sales SKUs, include all raw promotional information, and preprocess raw information using Principal Component Analysis. The empirical results obtained using daily data from a Portuguese retailer show that the inclusion of promotional information from SKUs in the same category may improve the forecast accuracy and that better overall forecasting results may be obtained if the best model for each SKU is selected.

Abstract
Sales forecasts gained more importance in the retail industry with the increasing of promotional activity, not only because of the considerable portion of products under promotion but also due to the existence of promotional activities, which boost product sales and make forecasts more difficult to obtain. This study is performed with real data from a Portuguese consumer goods retail company, from January 2012 until April 2015. To achieve the purpose of the study, dynamic regression is used based on information of the focal product and its competitors, with seasonality modelled using Fourier terms. The selection of variables to be included in the model is done based on the lowest value of AIC in the train period. The forecasts are obtained for a test period of 30 weeks. The forecasting models overall performance is analyzed for the full period and for the periods with and without promotions. The results show that our proposed dynamic regression models with price and promotional information of the focal product generate substantially more accurate forecasts than pure time series models for all periods studied.