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Moving averages is a forecasting method that uses the average of the k most recent data values in the time series as the forecast for the next period (Anderson, Sweeney, Williams, Camm, Cochran, Fry, & Ohlmann). This approach can be used when the company requires immediately forecasting for a massive volume of data. Exponential smoothing a forecasting method that uses a weighted average of past time series values as the forecast; it is a special case of the weighted moving averages method in which we select only one weight—the weight for the most recent observation. While Weighted moving averages a forecasting method that involves selecting a different weight for the k most recent data values in the time series and then computing a weighted average of the values, the sum of the weights must equal one (Anderson, Sweeney, Williams, Camm, Cochran, Fry, & Ohlmann).

The error measures are the mean square error (MSE), Mean absolute deviation (MAD), and mean absolute percentage error (MAPE). These errors will be used in the previous forecasting methods, where the least methods of errors will be considered the best forecasting techniques.

Answer 1

Moving averages is a statistical tool in simple time trend analysis. It shows how a variable moved, on average, the period of time. Moving averages are frequently used as a primary analysis to highlight trends, reversals, and provide a future signal for the forecast. There are several types of moving averages that smooth out a variation on average basic and generate single smooth line that depicts direction a variable movement over time.

The simple moving average (SMA) calculates an average of the last n period, which you want the average and mover further by replacing one past with one recent. It provides equal weight.   

Weighted moving averages a weighted average, that impose more weighting to more current data points since they are more relevant than data points in the distant past. The sum of the weighting should add up to 1. It is generally accepted form to given different weight to different observation. If one thinks recent past will explain recent future then it is appropriate.

Exponential Moving Averages are known as exponential smoothing seen as formula-driven weight. where the weighting decreases exponentially with each previous price/period. It uses an exponentially weighted vector to give more weight to recent prices. It is a better characterization of a time trend compared to a WMA or SMA. It is more responsive to changes over time in data. Hence it smoothes the data that can otherwise seem noisy. On the other hand, basic smoothing delivered by the SMA may provide an essential finding and quick support to forecast.

All these things and precise forecast depend upon forecast error. Lower the error more precise the fitting of a function average of exponential.

MSE measures the average squared difference between the estimated values and the actual value it is based on varince of actual and fitted values.

MAPE measures the size of the error in percentage terms and easy to interpret, MAP measures the size of the error in units. All measure have merits and demerits. The MAPE is sensitive to the size and should not be used when forecasting with low-sample of data. The MAPE and MAD are the most commonly used error measurement statistics, however, both can be misleading under certain circumstances.

Suppose we apply forecast based on 80% of data for rest 20% of data. so we first calculated SMA, WMA AND EMA then we calculated suppose all three forecast error.

So we need to first assess which forecast error method will be appropriate varies case to case basis and closely follow each other but not strictly comparable.  Next, we can choose the best method relied upon one of the forecast error methods.