Hobbies And Interests
Time Series Analysis
A time series is a sequence of data points in time, usually displayed as a graph or chart. Time series can be analysed manually by trying to discern any meaningful trend. An example of a time series is a patient's heartbeat. Because the trend of a "healthy" heartbeat is known, physicians can use time series analysis to check for irregular heartbeats. This sort of manual time series analysis is only suitable when there is a clean, noise-free signal and the underlying mechanisms generating the signal are well known.
Noise and Signal
Trend analysis is about identifying the signal in data. The signal is the meaningful pattern or trend in the data. In the real world there is often some random interference or "noise" that obscures the signal. Many trend estimation methods are attempts to filter out the noise and leave behind the meaningful signal. This signal can give an indication of the future trend of the data.
Simple Moving Average
The simple moving average is a trend estimation technique suitable for use on data that exhibits regular periodic changes. The simple moving average is used to determine if there is any long term trend in the data, whilst ignoring the periodic changes. An example would be the sales of a toy company. These sales would tend to peak every year around Christmas, so they will exhibit periodicity of one year. In order to find what (if any) trend exists in the long run, the toy company would use a simple moving average. Given a set of n data points 1,2, ... ,n-1,n the k-point simple moving average is found by plotting the mean average of each consecutive set of k consecutive data points:
(1,2,...,k-1,k)/k, (2,3,...,k,k+1)/k, ... ,(n-k,n-(k-1), ... ,n-1,n)/k.
This produces a smaller, smoother data set that shows the long term trend of the data and is used primarily to discern long term trends in data whilst filtering out seasonality.
Weighted Moving Average
The weighted moving average is similar to the simple moving average except that the average data points are each given a weight that reflects how significant they are believed to be. The determination of that weight is a subjective decision made on the basis of knowledge about the past behavior of the data set. One conventional method of selecting it is widely used in finance. In this convention, if the number of data point is "n" then the most recent data point is weighted my multiplying it by n, the previous data point is weighted as n - 1, and so on all the way back to the first data point, which is weighted as 1. The weighted moving average is suitable for estimating trends when the trends are likely to be most impacted by the more recent movements in the data. This can yield more accurate trend estimates in data sets where recent movement strongly impacts subsequent movements, such as financial market price data.
Exponential Smoothing Model
The exponential smoothing model, also called the exponential moving average, is a trend estimation technique that applies weights that decrease in an exponential fashion. The exponential smoothing model predicts the next data point in a series of given data points. This is calculated by multiplying the most recently observed data point and multiplying it by a weighting coefficient alpha, then adding this to (1 - alpha) multiplied by the exponential smoothing model prediction for the most recently observed data point:
ESM = alpha*X + (1 - alpha)*(ESM-1)
Where ESM is the predicted next value using the exponential moving average, alpha is the weighting constant, X is the most recently observed data value and ESM-1 is the exponential moving average estimate of the most recently observed data point. The exponential smoothing model amplifies the impact of the most recent values on the projected trend estimation. It is used in situations where the recent movements of the data set are significantly more important than earlier movements.