There are a few good books on it actually. You should look it up.
You need the data to be homoscedastic, the errors to be independent. The independent variable(s) should lie within (or very close to) the range of observed values.
Dan Henderson vs. Rashad Evans Prediction
A prediction is the strong belief that something will happen. It is said to be a true prediction if the event happens. Before the event takes place, you would have to ask the prophet/psychic making the prediction what it means. After the event, or after the prediction is proven false, you can see for yourself what it means.
The valid prediction range is the range of the "predictor."
They are interval.
There are many ways one might use Exponential Smoothing. Basically, Exponential Smoothing is a simple calculation one uses to collect data that allows one to predict future events.
When implemented digitally, exponential smoothing is easier to implement and more efficient to compute, as it does not require maintaining a history of previous input data values. Furthermore, there are no sudden effects in the output as occurs with a moving average when an outlying data point passes out of the interval over which you are averaging. With exponential smoothing, the effect of the unusual data fades uniformly. (It still has a big impact when it first appears.)
That, my friend, is not a question.
1) forecasting for stationary series A- Moving average B- Exponential Smoothing 2) For Trends A- Regression B- Double Exponential Smoothing 3) for Seasonal Series A- Seasonal factor B- Seasonal Decomposition C- Winters's methode
Confidence interval considers the entire data series to fix the band width with mean and standard deviation considers the present data where as prediction interval is for independent value and for future values.
Exponential Smoothing Model
what exponential function is the average rate of change for the interval from x = 7 to x = 8.
G. Kallianpur has written: 'White noise theory of prediction, filtering, and smoothing' -- subject(s): Gaussian processes, Kalman filtering, Prediction theory
The linear function changes by an amount which is directly proportional to the size of the interval. The exponential changes by an amount which is proportional to the area underneath the curve. In the latter case, the change is approximately equal to the size of the interval multiplied by the average value of the function over the interval.
Joseph V. Reilly has written: 'A dynamic inventory model using exponential smoothing'
Exponential smoothing is advantageous in marketing as it provides a simple and efficient method for forecasting demand by giving more weight to recent data, allowing for quick adjustments to changes in trends. It is particularly useful for short-term forecasting and can help optimize inventory levels and resource allocation. However, its disadvantages include the potential to overlook long-term trends and seasonality, as it primarily focuses on the most recent data. Additionally, if the data is highly volatile, exponential smoothing may produce unreliable forecasts.
Exponential moving average is a running average of a set of observations, where the weight of each observation is inversely exponentially weighted as a function of how old it is. It is a relatively simple thing to do. Given a set of observations O1, O2, O3, ... ON the running exponential moving average A1, A2, A3, ... AN can be calculated in real time, at each time N, with the expression ... AN = AN-1 (1 - X) + ON X ... where X is a weighting factor that determines that amount of smoothing. For instance, if X were zero, then the smoothing is infinite, and O does not contribute at all to A, and if X were one, then smoothing is zero, and A follows O with no smoothing at all. In a more useful example, if X were 0.2, then the smoothing would be five, and A would follow O with a time constant of five iterations, i.e. after five iterations we would be at about 63% of one step change and after 25 iterations we would be at about 95% of one step change.