Time Series Forecasting

A time series is a set of values for a sequence of random variables over time. Let Xy Xy Xy. .., X bc random variables denoting demands for periods 1, 2. n. The forecasting problem is to estimate the demand for period (n + 1) given the observed values of demands for the last n periods, Dy Dy. .., D . If is the forecast of demand for period (n + 1), then is the predicted mean of the random variable X y In other words. 

In quantitative forecasting, we assume that the time series data exhibit a systematic component, superimposed by a random component (noise). The systematic component may include the following  

Constant level with trend (growth or decline) Constant level with seasonality and trend 

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P. Deveka and L. Achenie, On the use of quasi-Newton based training of a feedforward neural network for time series forecasting. J. Intell. Fuzzy Syst., 3 (1995) 287-294. 

Regression analysis models and estimation theory models are very useful for the identification of mathematical relations and parameter values in these relations from sets of data or measurements. Regression and estimation methods are used frequently in conjunction with mathematical modehng, in particular with trend extrapolation and time series forecasting, and with econometrics. These methods are often also used to validate models. Often these approaches are called system identifi-... 

Keywords Bullwhip effect Supply chain management Multiagent system Time series forecasting... 

Mean absolute scaled error (MASE) To overcome the drawbacks of existing measures, Hyndman and Koehler (2006) proposed MASE as the standard measure for comparing forecast accuracy across multiple time series after comparing various accuracy measures for univariate time-series forecasting. MASE is expressed as follows ... 

De Gooijer, J. and Hyndman, R., 2006. 25 years of time series forecasting. International Journal of Forecasting, 22(3), 443 73. 

Tang, Z., Dealmeida, C. and Fishwick, R, 1991. Time-series forecasting using neural networks vs Box-Jenkins methodology. Simulation, 57,303-310. 

J. Gareth and S. Louise, Time Series, Forecasting, Simulations Applications, ElUs Harwood Limited, UK, 1993. 

A common set of forecasting techniques are called time-series forecasts. A time series is any group of data that is arranged in sequence according to the time it was gathered. For example, the monthly demand for a product is time-series data. There is a large number of time-series forecasting methods. We will examine only three of them. 

A second time-series forecasting method is the weighted moving average. Instead of simply taking the average of a set number of periods, this method weights the more recent periods heavier than the older periods. 

R. Aratijo, A. de. Swarm-based translation-invariant morphological prediction method for financial time series forecasting. Inf. Sd. 180, 4784-4805 (2010)... 

The second model which must be parameterized is the time-series forecast model. This is equivalent to determining the location (placement) of the demand curve for each customer segment for each product. The placement of the demand curve is of critical importance, since it represents the potential size of the market and whether or not supply constraints will bind. If demand from a market segment is large relative to supply, then the optimal prices are adjusted to reflect the opportunity cost associated with limited supply. 

Step 3 Select an appropriate time series forecasting method. 

Step 3 Select any time series forecasting method. For illustration, we will use the exponential smoothing forecasting method with a = 0.2.For the initial forecast for Quarter 1 of year 2008, we will use 600. 

Note that we could have used any of the time series forecasting method discussed in Step 3 of Section 2.4. 

National Car Rental (Geraghty and Johnson, 1997) Time series forecasting models with seasonality was used by National Car Rental to forecast customer demands for cars and estimate revenues. They were used in the company s revenue management system. 

In general there are two frequently used models for time series forecasting ... 

Time series Time-series forecasting methods use historical demand to make a forecast. They are based on the assumption that past demand history is a good indicator of future demand. These methods are most appropriate when the basic demand pattern does not vary significantly from one year to the next. These are the simplest methods to implement and can serve as a good starting point for a demand forecast. 

In the next section, we discuss techniques for static and adaptive time-series forecasting. 

Artificial Neural Networks (ANNs) have been deemed successful in applications involving classification, identiflcation, pattern recognition, time series forecasting and optimisation. ANNs are distributed information-processing systems composed of many simple computational elements interacting across weighted connections. It was inspired by the architecture of the human brain. The ability of ANNs to model a complex stochastic system could be utilised in risk prediction and decision-making research, especially in areas where multi-variate statistical analysis is carried out. 

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