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Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading.
Volume–price trend (VPT) (sometimes price–volume trend) is a technical analysis indicator intended to relate price and volume in the stock market.VPT is based on a running cumulative volume that adds or subtracts a multiple of the percentage change in share price trend and current volume, depending upon the investment's upward or downward movements.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...
As shown in the formula it reduces the weight on the recent values and by calculating ema of the ema we are trying to remove the weight on the long slower part of the average that has built up over time. It significantly helps make quicker decisions than the simple MA crossovers.
There have also been proposed methods for adjusting the smoothing constants used in forecasting methods based on some measure of prior performance of the forecasting model. One such approach is suggested by Trigg and Leach (1967), which requires the calculation of the tracking signal.
If the trend can be assumed to be linear, trend analysis can be undertaken within a formal regression analysis, as described in Trend estimation. If the trends have other shapes than linear, trend testing can be done by non-parametric methods, e.g. Mann-Kendall test, which is a version of Kendall rank correlation coefficient.
The model was based on a linear regression model, and is used to measure linear trends based on seasonal cycles and their affects on demand i.e. the seasonal demand for a product based on sales in summer and winter. The linear regression model is described as: = + +