Forecasting own brand sales: Does incorporating competition help?

This study aims to investigate how much value is added to traditional sales forecast- ing models in marketing by using modern techniques like factor models, Lasso, elastic net, random forest and boosting methods. A benchmark model uses only the focal brand's own information, while the other models include competitive sales and market- ing activities in various ways. An Average Competitor Model (ACM) summarises all competitive information by averages. Factor-augmented models incorporate all or some competitive information by means of common factors. Lasso and elastic net models shrink the coecient estimates of specic competing brands towards zero by adding a shrinkage penalty to the sum of squared residuals. Random forest averages many tree models obtained from bootstrapped samples. Boosting trees grow many small trees sequentially and then average over all the tree models to deliver forecasts. We use these methods to forecast sales of packaged goods one week ahead and compare their pre- dictive performance. Ou

Bootstrap Approximation to Prediction MSE for State-Space Models with Estimated Parameters

We propose a simple but general bootstrap method for estimating the Prediction Mean Square Error (PMSE) of the state vector predictors when the unknown model parameters are estimated from the observed series. As is well known, substituting the model parameters by the sample estimates in the theoretical PMSE expression that assumes known parameter values results in under-estimation of the true PMSE. Methods proposed in the literature to deal with this problem in state-space modelling are inadequate and may not even be operational when fitting complex models, or when some of the parameters are close to their boundary values. The proposed method consists of generating a large number of series from the model fitted to the original observations, re-estimating the model parameters using the same method as used for the observed series and then estimating separately the component of PMSE resulting from filter uncertainty and the component resulting from parameter uncertainty. Application of the method to a model fitted to sample estimates of employment ratios in the U.S.A. that contains eighteen unknown parameters estimated by a three-step procedure yields accurate results. The procedure is applicable to mixed linear models that can be cast into state-space form. (Updated 6th October 2004

Evaluating the German Inventory Cycle Using Data from the Ifo Business Survey

Inventory fluctuations are an important phenomenon in business cycles. However, the preliminary data on inventory investment as published in the German national accounts are tremendously prone to revision and therefore ill-equipped to diagnose the current stance of the inventory cycle. The Ifo business survey contains information on the assessments of inventory stocks in manufacturing as well as in retail andwholesale trade. Static factor analysis anda methodbuild ing on canonical correlations are appliedto construct a composite index of inventory fluctuations. Based on recursive estimates, the different variants are assessedas regards the stability of the weighting schemes andthe ability to forecast the "true" inventory fluctuations better than the preliminary official releases. --inventory investment,revisions,composite indices,canonical correlation,factor models,national accounts data,Ifo business survey,Germany

Forecasting the unemployment rate using the degree of agreement in consumer unemployment expectations

This study aims to refine unemployment forecasts by incorporating the degree of consensus in consumers' expectations. With this objective, we first model the unemployment rate in eight European countries using the step-wise algorithm proposed by Hyndman and Khandakar (J Stat Softw 27(3):1-22, 2008). The selected optimal autoregressive integrated moving average (ARIMA) models are then used to generate out-of-sample recursive forecasts of the unemployment rates, which are used as benchmark. Finally, we replicate the forecasting experiment including as predictors both an indicator of unemployment, based on the degree of agreement in consumer unemployment expectations, and a measure of disagreement based on the dispersion of expectations. In both cases, we obtain an improvement in forecast accuracy in most countries. These results reveal that the degree of agreement in consumers' expectations contains useful information to predict unemployment rates, especially for the detection of turning points

Macroeconomic Forecasting with Mixed Frequency Data : Forecasting US output growth and inflation.

Although many macroeconomic series such as US real output growth are sampled quarterly, many potentially useful predictors are observed at a higher frequency. We look at whether a recently developed mixed data-frequency sampling (MIDAS) approach can improve forecasts of output growth and inflation. We carry out a number of related real-time forecast comparisons using various indicators as explanatory variables. We find that MIDAS model forecasts of output growth are more accurate at horizons less than one quarter using coincident indicators ; that MIDAS models are an effective way of combining information from multiple indicators ; and that the forecast accuracy of the unemployment-rate Phillips curve for inflation is enhanced using the MIDAS approach.Data frequency ; multiple predictors ; combination ; real-time forecasting

Evaluating the German Inventory Cycle – Using Data from the Ifo Business Survey

Inventory fluctuations are an important phenomenon in business cycles. However, the preliminary data on inventory investment as published in the German national accounts are tremendously prone to revision and therefore ill-equipped to diagnose the current stance of the inventory cycle. The Ifo business survey contains information on the assessments of inventory stocks in manufacturing as well as in retail and wholesale trade. Static factor analysis and a method building on canonical correlations are applied to construct a composite index of inventory fluctuations. Based on recursive estimates, the different variants are assessed as regards the stability of the weighting schemes and the ability to forecast the “true” inventory fluctuations better than the preliminary official releases.inventory investment, revisions, composite indices, canonical correlation, factor models, national accounts data, Ifo business survey, Germany

Understanding the Kalman Filter: an Object Oriented Programming Perspective.

The basic ideals underlying the Kalman filter are outlined in this paper without direct recourse to the complex formulae normally associated with this method. The novel feature of the paper is its reliance on a new algebraic system based on the first two moments of the multivariate normal distribution. The resulting framework lends itself to an object-oriented implementation on computing machines and so many of the ideas are presented in these terms. The paper provides yet another perspective of Kalman filtering, one that many should find relatively easy to understand.Time series analysis, forecasting, Kalman filter, dynamic linear statistical models, object oriented programming.

Macroeconomic Forecasting with Mixed Frequency Data: Forecasting US Output Growth

Many macroeconomic series such as US real output growth are sampled quarterly, although potentially useful predictors are often observed at a higher frequency. We look at whether a mixed data-frequency sampling (MIDAS) approach can improve forecasts of output growth. The MIDAS approach is compared to other ways of making use of monthly data to predict quarterly output growth. The MIDAS specification used in the comparison employs a novel way of including an autoregressive term. We find that the use of monthly data on the current quarter leads to significant improvement in forecasting current and next quarter output growth, and that MIDAS is an effective way of exploiting monthly data compared to alternative methods. We also exploit the best method to use the monthly vintages of the indicators for real-time forecasting.Mixed data frequency, Coincident indicators, Real-time forecasting, US output growth