Elements of Forecasting - A Case Study:
German Car Production

von: Maria Kimme

Table of Content

1. Introduction page 3

2. Introduction of the Series page 4

3. Modelling a Univariate Model page 6

3.1 Trend Analysis page 6
3.2 Seasonal Analysis page 8
3.3 Cyclical Analysis page 9
3.4 Evaluation of the ARMA Model page 10
3.5 The Unit-Root Test page 11
3.6 The ARIMA Model page 11

4. Modelling a Multivariate Model  page 14

5. Conclusion  page 16

6. Bibliography  page 17

Appendices A till G  page 18

1. Introduction

Forecasting is one of the mayor issue in today’s business world. Whether it concerns the economic situation, stock prices, or production levels, a glance into the future would be very valuable. By excluding uncertanties, expenses can be saved and revenues be generated. Unnecessary or too little inventories, capacity standing idle or being short, missing raw materials or too many employees are just some of the situations, which lead to lower profits. Hence, perfect forecasts would be worth a lot of money. But, as the expression states, a “perfect forecast” is a paradox, since the future will stay uncertain till the moment, where it becomes the present. As the American philosopher Eric Hoffer once stated: “The only way to predict the future is to have the power to shape the future”, which would take place in the present. The one chance we have in making inferences about the future, is to incorporate logic, intuition, and experience into models, which will then – if we are lucky, that is – produce more or less accurate forecasts.

Forecasting, if pursued by professionals, relies mainly on past data, since those are the most reliable source of unbiased information. Applying econometric models will then lead to results, which can be tested for their stability and for reliability, especially when compared to actual data. This procedure will be presented during the following paragraphs with the help of an example, namely the number of cars produced in Germany every month. I chose this data set out of two reasons. Firstly, these industry is one of the most important industries within the German economy, and secondy, my professional engagement with a car-producing company provides my with some insight into the industy.

In order to generate forecasts, the model will build upon systematic components, such as trends, seasonality, and cyclicality. Furthermore, concepts like moving averages and autoregressions will be incorporated into the model. Following, the data will be tested, whether it returns to it mean after experiencing a shock. This will be done via a unit-root test. In case of its occurrence, the unit-root will be removed by a stochastic model. Next, a second series will be introduced, the collection of leading indicators for the German economy, and incorporated. According tests towards the causal relationship will be provided and a forecast will be suggested on the basis of a multivariate model. Concluding, the two forecasts will be compared.

2. Introduction of the Series

The automotive industry is one of the most important in the German economy, which can easily be seen on the number of domestic brands, such as Mercedes-Benz, Audi, Volkswagen, and BMW. But due to the globalization, those formerly German companies turned into international, if not global enterprises. Therefore, some of the firms’ products are assembled abroad, while foreign companies (e.g. Ford) produce now within German borders. Thus the presented series encorporated the cars produced in Germany. By looking at the data, one can see that the production of cars increased during the last Years four centuries. The high variability, which obviously indicates seasonality, is also worth mentioning. A third observation are the cycles the series describes, which seems to follow the business cycle of the German economy. But these observations should be underlined with some scientific evidence. As can be seen from figure 2, the distribution seems to be normal. Firstly, the mean, the median, and the mode do not differ too much from each other, indicating a normal distribution. Secondly, the skewness coefficient of –0.076477 underlines this finding. Thirdly, the kurtosis value of 2.261076 indicates a little flatter tails then normal. Finally, the Jarque-Bera test examines the hypothesis of independent normally distributed observation. The reported probability rejects it in favor of the alternative hypothesis. This leads to the conclusion that the data provide a good basis for an analytical forecast.

3. Modelling a Univariate Model

3.1 Trend Analysis

Most data series exhibit a trend. Underlying this trend is usually some kind of growth, such as inflation, population growth, or increases in wealth. But these trend do not always have to be linear. Most stock market indices increased exponentially, while learning curves are not seldomly u-shaped (one would speak here of a quadratic trend). As stated before, the data at hand also seems to follow a trend. This section will be used to test the data for the occurrence of a linear, quadratic, exponential, or polynomial trend. But before, the underlying statistics of these models will be introduced:

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