So, hi, everyone and welcome to this video. The second video in our series for univariate forecasting in our and in this video we’re gonna test for non stationarity, so we’re gonna conduct three tests for a non stationarity, so we know that to be able to implement Ar MA and ARMA okay to a non stationary series. We would need a different still the series. So what we’re gonna do now is we need to determine okay, whether or not the series that we have, which is inflation in this case is stationary or non stationary and the way we do that is through testing, so we have three tests to use today. The first is the augmented dickey-fuller. The second is the Philips Padron and the third is the K Pss test, so we’re going to use these three tests to try and detect non stationarity, so let’s start with the augmented dickey-fuller test augmented dickey-fuller and the the augmented. Dickey-fuller is a unit root test, meaning the null hypothesis of this. This test is non stationarity and the alternative is stationarity. So if we reject the null, then the series must be stationary And I’m gonna caution you at that before. We even start that there is a weakness to the augmented dickey-fuller test in that. You have to specify, okay. The lab order the test in general is not a generalized test, meaning we would need to try and specify lab orders to see actual things, and after all result, it can do it by default and we’ll show that first, but the results may be misleading If we don’t specify a desired lab order, so I’ll show that in this example, so the command to invoke the augmented dickey-fuller test is a BF dot test and that’s a dia test run in when inflation, so lets. Just see that now, if you notice. Kay, I ran in a while back, but I rerun it again. And we found that the result of the test. Okay, is that inflation is stationary at level now. That’s very, that’s very curious and that it doesn’t seem like. Inflation is stationary at level and the reason for that is because it shows a lot of order of six. Okay, notice we have a log order six. Now it’s not absurd that we have high lag orders, but generally, when we’re dealing with inflation data, at least for the context of the Philippines, the log order tends to be low and maybe one or two, so let’s test the result of the test when we specify the log to be one or two. So that’s a DF test, okay, in, okay, and to specify a log order, we use K so say, I specify two logs, which is the most normal lag that we use so forecasting inflation. Based on my experience we use to log so here and we notice that when we specify the lag okay off to, we fail to reject the null hypothesis, and it suggests that the series is non stationary, so that’s one of the key, our weaknesses of the augmented dickey-fuller test and that it’s not that generalized and you have to specify the line order, so let’s try it with using a log of one so ADF test and K is equal to 1 Okay, and we have that one. And when we specify one, the p-value is even higher, okay, which suggests that the series is more non stationary. Okay, because as you increase the laboratory, generally, the series becomes more and more stationary, but typically that the the correct lock order to use is 1 or 2 so the series is non stationary, but we could get a stationary result, which could be very deceiving because we then specify the lock order so as a check. Let’s try and just check if the difference is. The difference of inflation is stationary, so this should be stationary at whatever log order by theory, and we find that. Yeah, okay, and at this lag order, the series is already stationary, so that’s the augmented dickey-fuller so what we want to do now we want to try and compare the three tests and see if they agree with each other and in general, you should you should see that. These three tests generally agree with each other, so let’s go to the Philips parent S Philips pair on test. Okay, so the command for the Philips parent S is PP dot test and we’re gonna do that on in now compared to the augmented dickey-fuller. We don’t need to specify the lock order for this for this test because it’s a more general test, so let’s do that, and we find that the series is non-stationary is non-stationary and it arbitrarily chose this, and since the more generalized s, it could kind of figure out which lock order to use in some cases, and we found that the series was non stationary. Which is what we expect rates what we expect and we could do a. Phillip’s parent test as well on the difference value of inflation. So that’s the end, and we find that, of course, it’s as expected. It is gonna be a stationary, non stationary. I’m sorry, stationary, rather, so that makes sense and then the last test we’re gonna do is the K PSS test. Okay, so that’s that quite Kowski. Philip’s midship! That’s quite a mouthful, so I won’t even try another time, so that’s a KP SS this and this one, okay, it’s a bit different from the other two tests in that. The null hypothesis of this test is stationary is that the series is stationary and its alternative. Hypothesis is non stationarity because this test is a stationarity test while the Philips Parata and the augmented dickey-fuller are unit root tests, so they they’re fundamentally, they’re fundamentally testing the same thing. It’s just that they have a different approach to doing that, so let’s use the KP SS test. So this is KP SS test and we’re gonna do our inflation and we find that. Yes, it is since we rejected the P value and this is the KP SS test. The series is non stationary, so if there is evidence that we would need to difference the series ones because all the three tests agree that the series at level inflation at level is non-stationary. Therefore, I would expect that the order in the Arima of integrated order or I there is gonna be equal to one because the series is stationary at the first difference. So let’s see if I’m correcting my hypothesis in the next video, then let’s do one final test this time on the different inflation, then we should expect that this one should not reject the null of stationarity and there’s something curious here. We find that that’s not the case, so according to the KP Sss. It still thinks that the difference series is a non stationary, so there are those cases and we have to deal with them so for now. These are the tests for non stationarity and in the next video. We’re going to start with our modeling and lets. See if the forecast goes. Well, so thank you.