Analytics-University
This video segment focuses on the concept of stationarity in time series data and the problems that non-stationarity can bring for forecasting. The video explains the difference between deterministic and stochastic trends and emphasizes the importance of understanding stochastic trends in non-stationary time series models, particularly in the case of a random walk process. The Dickey-Fuller test is introduced as a statistical test used to determine if a time series is unit root or not, and the three different types of the Dickey-Fuller test are discussed with their corresponding null hypotheses. The speaker advises against using sophisticated methods for forecasting if the time series follows a random walk.
In this section of the video, the presenter discusses the concept of stationarity in time series data and how non-stationarity can bring problems for forecasting. Stationarity is when a time series has a constant mean and variance, which are two important factors to determine if a time series is stationary. Non-stationarity can occur when either the mean or variance (or both) are non-constant, which can be problematic for forecasting. The video focuses on non-stationarity in the mean, and introduces the concept of deterministic and stochastic trends in time series data. Deterministic trends are easier to handle as they are an explicit function of time, while stochastic trends are more difficult to manage as they are uncertain.
In this section of the video, the narrator explains the difference between a deterministic trend and a stochastic trend in a time series model. A deterministic trend is a known, upward trend that can be calculated based on time. In contrast, a stochastic trend is uncertain and is a function of its previous values. The narrator uses equations and simulations to demonstrate the difference between the two trends and how they can be handled differently when the modulus of the slope parameters is equal to 1. The video emphasizes the importance of understanding stochastic trends in non-stationary time series models.
In this section, the concept of non-stationary time series is discussed. The case of interest is when the modulus of Phi equals 1, which is a form of random walk. The series becomes mean-reverting when Phi is less than 1, meaning it will come back towards its mean whenever it goes up. However, when Phi equals 1, it is a typical case of a random walk model, where the series has no pattern, and is just pure random noise, making it difficult to use for forecasting future values. The random walk process is found in many areas such as finance and science, and it is the limiting process of an AR one process.
In this section, the video discusses the concept of a random walk process and how it is related to unit root and a stochastic trend series. The speaker explains that random walk is a special case of the air one process, where the best prediction for the future value is the current value. If a time series data follows a random walk, there is nothing more that can be done than to predict the current value. The video also introduces the Dickey Fuller test, a statistical test used to determine if a time series is unit root or not. The simplest approach to the test is through the air one series, where the modulus of Phi is either one or less than one, with less than one being the alternative hypothesis.
In this section, the three types of Dickey-Fuller test are discussed, which depend on the kind of random walk that is being analyzed. The first case is a pure random walk, the second one includes a drift, and in the third case, there is a drift and a deterministic time component. The null hypothesis now could either be zero or less than B. To find a test statistic, apply OLS, estimate the parameters, find Phi, and then find out the T statistics to see if it is significant. The results cannot be used to forecast the future but are useful in understanding the past values of the time series for forecasting purposes. If it is a random walk, then it is advised not to proceed with sophisticated methods for forecasting, which will save time.
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