Detecting Trends from Accumulated Changes in the Prices of a Stock

Abstract

The paper presents a method to segment a time series by using trends estimated on it, trends that are formed by peaks and troughs produced by runs of increments and decrements. Each run measures the relative change produced by accumulating the increments or decrements from the previous run. A time series of daily stock prices is used to demonstrate the method. A series of consecutive price changes in the increasing or decreasing direction constitutes a run in the prices. In this view a run is broken when prices are repeated. Runs of price increases or decreases is used to estimate an increasing or decreasing trend in the prices. The trend is estimated between two points in the time series and relates the amount of accumulated change between the points to the number of data points between them. The main contributions of the paper include a method to estimate the amount of linear change between the two points by using this accumulated change between two points in time. The linear change between the two points corresponds to an estimate of the average change in prices at each price change. A trend estimated over such runs in the prices also provides an estimate for the rate of return. It also provides an estimate for the average rate over time at which the prices rise or fall. The method also detects the size of a relative change in direction in the time series. This model of the trend is used to segment a time series of stock prices by detecting changes in the trend. It serves as visual means to trade in the stock by providing information about the persistence of a series of price rises or falls, the relative size of each rise, fall or trend, the time interval of the trend and the rate at which trends change.