Time-series forecasting methods

The goal of any forecasting method is to predict the systanatic component of danand and estimate the random component. In its most general form, the systematic component of demand data contains a level, a trend, and a seasonal factor. The equation for calculating the systematic component may take a variety of forms  

The specific form of the systematic component applicable to a given forecast depends on the nature of demand. Companies may develop both static and adaptive forecasting methods for each form. We now describe these static and adaptive forecasting methods. 

A static method assumes that the estimates of level, trend, and seasonality within the systematic component do not vary as new demand is observed. In this case, we estimate each of these parameters based on historical data and then use the same values for aU future forecasts. In this section, we discuss a static forecasting method for use when demand has a trend as well as a seasonal component. We assume that the systematic component of demand is mixed that is. 

Systematic component = (level -l- trend) X seasonal factor 

A similar approach can be applied for other forms as well. We begin with a few basic definitions  

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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. 

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. 

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. 

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-... 

If data of the real system is available, the developed simulation model can be tested for similarity with the real system in a qnantitative way (bottom-right cell in Table 4.8). For this purpose, a lot of statistical procedures can be applied depending on the specific object to be tested. Typically, regression techniqnes, distribution tests, or time series analysis methods are used. A reliable qnantitative approach is to generate a forecast of the near future by means of the simulation model which is then compared with the real systems behaviour after the forecast period has expired. This is called predictive validation A mixture of trace analysis and fixed-value test is the trace-driven simulation where a historical situation is simulated. The model s output is compared with the historical records then. 

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

The structural time series analysis methods also referred to as state-space methods [HAR 86, COM 07] have been used more and more for modeling the aggregate number of fatalities at national level [DUP 07], The approach that the authors adopt is innovative, as usually such analyses are led on an annual basis - in order to explain and forecast long-term changes in the aggregate number of fatalities at national level [LAS 01]). On the contrary, short-term changes can only be modeled on an infra-annual basis similar but uncompleted approaches were taken on a quarterly basis - without the inclusion of exogenous variables [COM 2007] and on a monthly basis - without the inclusion of economic variables [BER 13]. 

It is also a form of time series analysis, which is a growth point in statistics. It is to be expected that as improved and novel statistical methods are developed, accumulated data will be used increasingly for the purposes of quality control and forecasting performance. 

Moving average. These methods try to eliminate randomness in a time series and smooth the curve of the data. This method of forecasting tends to lag a trend, and the more periods included in the average, the greater the lag will be. This method is best suited for products that have a stable demand. 

Brown s ejqtonential smoothing method is used for forecasting time series data that have a linear trend. This method is similar to double moving average techniques. Only one smoothing constant is used in this method. 

The time series analysis is a statistical method to reveal the dynamic law of a system through dynamic data (Box 2005). Its core idea is that, with the finite number of data in the series, a model could be created to precisely reflect the dynamic relationship hided in the time series, and then to forecast the future. 

The original data which this paper used to research was time series Si) t) of CBM productivity of Yuyang coal mine. The method of wavelet prediction and the AR model of time series were separately used for different samples to forecast, and forecast results were compared and analyzed. 

Grrey prediction method is based on the grey modules, and using differential fitting method to establish the accumulation model. It is mainly used in forecasting of single variable time series (Hu 2007, Liu et al. 2007). The GM (1,1) model is a concrete application of the grey prediction method its basic formula is as follow ... 

Univariate Forecasts of a given variable demand are based on a model fitted only to present and past observations of a given time series. There are several different univariate models, like Extrapolation of Trend Curves, Simple Exponential Smoothing, Holt Method, Holt-Winters Method, Box-Jenkins Procedure, and Stepwise Auto-regression, which can be regarded as a subset of the Box-Jenkins Procedure. 

All of the time-series methods are used for short-term forecasts. They are used to calculate the demand for the next period. 

Quantitative forecasting methods require historical data that are accurate and consistent. They assume that past represents the future, namely, history will tend to repeat itself. Most quantitative methods fall in the category of time series analysis and are discussed in detail in Section 2.4. 

Consider again the 6-month time series data on demand given in Table 2.4. We will apply Holt s method to determine the forecast for month 7. In order to get started with Holt s method, we need the... 

Automatic software These are designated stand alone programs and may cost thousands of dollars. The user does not have to be proficient in forecasting. The soffware asks fhe user to enter the time series data. It selects the appropriate method based on the analysis of the data and recommends a forecasting method. It also computes the optimal values of fhe parameters (e.g., smoothing constants a, P, and y for Winters method) using forecast errors. It then... 

Semi-automatic software These are moderately priced but they require the user to have some basic knowledge of forecasting principles and fechniques. Here, fhe user has to select an appropriate forecasting technique based on the analysis of time series data. The software will then compute the optimal parameters for the chosen method using some measure of forecasf error. It also gives the forecasts and all the statistics, such as MAD, MAPE, MSE, Bias, etc. The software makes no recommendation as to which forecasting technique is appropriate for the given data. 

Several forecasting methods have been adopted by the garment industry. The most commonly used methods are generic statistical time series models such as ... 

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