Transcript:
Our tutorial augmented dickey-fuller test first-order. Train stationary time Series consists of random processes that have constant mean which don’t exhibit trend pattern. This topic is part of first trading analysis with our curse feel free to take a look at curse curriculum by clicking link that description box below this tutorial has an educational and informational purpose and doesn’t consider any type of training or investment advice. Please read full tutorial disclaimer. At the end of this video, augmented dickey-fuller test consists of evaluating whether Time’s use was first-order. Train stationery, What null hypothesis that it had a unit root and was not stationary for full reference. I recommend you read David Decay and Wayne Fuller distribution of the Estimators for auto regressive time series with a unit root published in Journal of American Statistical Association in 1979 As a formula, we have that current period data difference is equal to a constant, plus a beta coefficient multiplied by a trend barble. This trend bar was a sequence from 1 all the way into the number variations, plus a gamma coefficient multiplied by previous previous data. Plus, and here we have the sum from the first two that. P number of lags included with an augmented dickey-fuller test of Delta coefficients multiplied by previous periods data difference, plus this regression forecasting errors or residuals. I’m regarding augmented dickey-fuller test. We have the following options first. C equals to 0 and beta equals to 0 therefore augmented dickey-fuller test without a constant and without a trend, verbal second option C different to 0 and beta equals to 0 therefore augmented dickey-fuller test with a constant but without a trend parable. And then we have C different to 0 and B that different to 0 therefore augmented dickey-fuller test with a constant and with a trained variable, and then we have individual tests for gamma coefficient. T statistic approximate a p-value. If gamma coefficient is S is the approximated P value was less than alpha percentage level of statistical significance. Then time series was first order train stationary with 1 minus alpha percentage level of statistical confidence on the other hand, if gamma coefficient. T statistic approximated P value was greater than alpha percentage level of statistical significance, then higher differentiation order needed for first order train stationary time series with 1 minus Alpha percentage level of statistical confidence notice that we can also perform adjoint test of the constant beta and gamma coefficients through F statistic approximated p-value if they were included with an augmented dickey-fuller test. Great, so let’s go back into our studio so that we can study augmented dickey-fuller test with greater detail. Hey, excellent, so here. We are within our studio. In this tutorial. We’ll be working with in our tutorial. Augmented dickey-fuller test code file so the first step where the tutorial is to load its packages, so we do so with library function and within it, the package name for this tutorial, we’ll be using 1 Mod and T series, so we select those two code lines then with Lebron or content and keyboard, which is equivalent, the following step is to create data for augmented dickey-fuller test and this is done through data reading, so we create this object named data, which is equal to read Dot Csv and within we have the name of the data file augmented dickey-fuller test data as a plain text file without CSV or comma separated values stored within the working directory comma header equals to true, so we select that code line, then click run or contents on the keyboard and notice that this created data object as a data frame within this global environment, so we click on the spreadsheet kind of icon and it opens the data for us. We have two columns of data first of this dates with a daily frequency from the beginning of 2007 all the way to the end of 2016 there are 4 10 years of data, and then we have. EWG adjusted EWG corresponds to the ETF investment vehicle, which intends to replicate the MSCI country index and adjust it because this includes adjusted clothes prices, which were adjusted for dividends and splits so back into the code file. What we’re going to do next is we’re going to convert that data frame into an XTS, which stands for extensible time series. So we overwrite data as an X Ts and from data, we select the second column with those at user close prices comma ordered by equals as date with capital. T data the first one with those dates and we’re going to rename the column names of data with GE R for those German prices. So we select the two code lines. Click run or ctrl enter on the keyboard and notice that it now became an X ES or extensible Time Series 10 If we open the data, we see that now. The dates became the index so back into the code file. The following steps were going to delimit training and testing ranges, training range, commonly used for Presidenta, fication and / spread cointegration evaluation and testing range, commonly used for purse trading strategies, calculation and their performance evaluation notice that this training and testing ranges, the limiting was only included as an example for educational purposes. Therefore, it is not fixed and it can be modified, according to units, so we create this object named T Data T for training range is going to be data from the beginning of the time series all the way to the end of 2014 there are for the first eight years of data, and then we create F data F for testing range and it’s going to be data from the beginning of 2015 all the way to the end of 2016 therefore, the last two years of data, so we select the two code lines click on contents on the keyboard and we create the two objects and in this tutorial, we’ll only be working within the training range. So the following step is to visualize prices within the corresponding chart, so we create this new object, which is going to be named TJR for German prices with training range equal to T. Data were going to plot those German prices women trained range with a corresponding title, So we select the two code lines here and we click run or confluence on the keyboard so now we can see start here within the corresponding area, so we’re going to zoom into it, and we see those German prices within the train range prices chart on the vertical axis. We have the adjusted closed prices on the horizontal one dates from the beginning of 2007 Although into the end of 2014 there are for the first eight years of data or the training range. So we close the chart there am The following step is to do the prices up mented dickey-fuller test were using this function, a DF test dot test and we’re using German price limit training range with the alternative, which is stationary and K equals to one that’s. The number of lags include with an augmented dickey-fuller test notice that this alternative parameter and number of lags were all included as an educational example. Therefore they are not fixed and they can be modified, according to units. So we select this cold line here and click run or contents on the keyboard and notice that within the console augmented dickey-fuller test results were printed the data. German price will enter a range dickey-fuller test statistic number of lags included here with the corresponding parameters of the function, as well as a stationery alternative hypothesis. And then we have the p-value. This augmented dickey-fuller test was done, including a constant and also including a trend, and the p-value is the one corresponding to that individual test described within the slights. Excellent, so now that we finished starting out meant Aditi fuller test, Let’s go back into the slides and as men Previously, this tutorial has an educational and informational purpose and doesn’t constitute any type of trading or investment advice. Please pause the video now. So you can read the full tutorial disclaimer. OK, so with this, we finish this tutorial. Thank you for watching.