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Date Created: 11/15/15
"Forecasting Models” Please respond to the following: What is the difference between a causal model and a time series model? Give an example of when each would be used. Casual forecasting methods are subject to the discretion of the forecaster. There are several informal methods which do not have strict algorithms, but rather modest and unstructured guidance. One can forecast based on, for example, linear relationships. If one variable is linearly related to the other for a long enough period of time, it may be beneficial to predict such a relationship in the future. This is quite different from the aforementioned model of seasonality whose graph would more closely resemble a sine or cosine wave. The most important factor when performing this operation is using concrete and substantiated data. Forecasting off of another forecast produces inconclusive and possibly erroneous results. Some forecasting methods use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast. For example, including information about weather conditions might improve the ability of a model to predict umbrella sales. This is a model of seasonality which shows a regular pattern of up and down fluctuations. In addition to weather, seasonality can also be due to holidays and customs such as predicting that sales in college football apparel will be higher during football season as opposed to the off season. Time series forecasting is the use of a model to predict future values based on previously observed values. Time series data have a natural temporal ordering. This makes time series analysis distinct from other common data analysis problems, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural oneway ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values. Time series are very frequently plotted via line charts. Wikipedia. (n.d.). Retrieved from http://en.wikipedia.org/wiki/Forecasting Time series. (08oc). Retrieved from http://en.wikipedia.org/wiki/Time_series What are some of the problems and drawbacks of the moving average forecasting model? A moving average forecast model is based on an artificially constructed time series in which the value for a given time period is replaced by the mean of that value and the values for some number of preceding and succeeding time periods. As you may have guessed from the description, this model is best suited to timeseries data; i.e. data that changes over time. For example, many charts of individual stocks on the stock market show 20, 50, 100 or 200 day moving averages as a way to show trends. One of the drawbacks to this model is forecast value for any given period is an average of the previous periods, then the forecast will always appear to "lag" behind either increases or decreases in the observed (dependent) values. For example, if a data series has a noticeable upward trend then a moving average forecast will generally provide an underestimate of the values of the dependent variable. The moving average method has an advantage over other forecasting models in that it does smooth out peaks and troughs (or valleys) in a set of observations. However, it also has several disadvantages. In particular this model does not produce an actual equation. Therefore, it is not all that useful as a mediumlong range forecasting tool. It can only reliably be used to forecast one or two periods into the future. Gould, S. (2011). Class movingaveragemodel. Retrieved from http://openforecast.sourceforge.net/docs/net/sourceforge/openforecast/models/MovingAv erageModel.html How do you determine how many observations to average in a moving average model? A moving average is a set of numbers, each of which is the average of the corresponding subset of a larger set of datum points. Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by "shifting forward", that is excluding the first number of the series and including the next number following the original subset in the series. This creates a new subset of numbers, which is averaged. This process is repeated over the entire data series. The plot line connecting all the (fixed) averages is the moving average. A moving average may also use unequal weights for each datum value in the subset to emphasize particular values in the subset. Wikipedia. (2011). Retrieved from http://en.wikipedia.org/wiki/Moving_average How do you determine the weightings to use in a weighted moving average model? A weighted average is any average that has multiplying factors to give different weights to data at different positions in the sample window. Mathematically, the moving average is the convolution of the datum points with a fixed weighting function. One application is removing pixelisation from a digital graphical image. In technical analysis of financial data, a weighted moving average (WMA) has the specific meaning of weights that decrease in arithmetical progression. In an nday WMA the latest day has weight n, the second latest n − 1, etc., down to one. WMA weights n = 15 The denominator is a triangle number equal to In the more general case the denominator will always be the sum of the individual weights. When calculating the WMA across successive values, the difference between the numerators of WMA M+1 and WMA iM np M+1 − pM − ... −M−n+1 If we denote the sum M + ... +M−n+1by TotalM, then The graph above shows how the weights decrease, from highest weight for the most recent datum points, down to zero. It can be compared to the weights in the exponential moving average which follows. Wikipedia. (2011). Retrieved from http://en.wikipedia.org/wiki/Moving_average
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