The series is stationary according to both ADF and KPSS test for stationarity.
However, both ACF and PACF plot still show significant lags.
Why is that?
Related
For a project I need to use the SARIMA model. I have read that before I train the model I need to perform a Dickey Fuller test to confirm that the data is stationary and I also read that I should plot the autocorrelation and partial autocorrelation to determine the best parameters for the model.
I would like some help with interpreting the plots.
Image of autocorrelation plots
It is clear that the 'lollipops' represent the correlation between the present value and the lag/k interval value, I also understand that the light blue area depicts the 95% confidence interval with significance testing but the relationship between the lollipops and the light blue area is unclear to me.
How can I use this plot to determine the parameters which I should use to build my SARIMA model?
I got weird ACF and PACF graphs for which the spikes do not lay within the shaded region. My data is stationary. I could not find a sharp shut-off in the ACF graph, so I could not determine the q value for my ARIMA model. Does anyone know what causes the graphs to look like this and what I should do? Any comments will be appreciated!
My ACF and PACF graphs
My stationary data looks like this
Im a beginner in time series analyses.
I need help finding the SARIIMA(p,d,q,P,D,Q,S) parameters.
This is my dataset. Sampletime 1 hour. Season 24 hour.
S=24
Using the adfuller test I get p = 6.202463523469663e-16. Therefor stationary.
d=0 and D=0
Plotting ACF and PACF:
Using this post:
https://arauto.readthedocs.io/en/latest/how_to_choose_terms.html
I learn to "start counting how many “lollipop” are above or below the confidence interval before the next one enter the blue area."
So looking at PACF I can see maybe 5 before one is below the confidence interval. Therefor non seasonal p=5 (AR).
But I having a hard time finding the q - MA parameter from the ACF.
"To estimate the amount of MA terms, this time you will look at ACF plot. The same logic is applied here: how much lollipops are above or below the confidence interval before the next lollipop enters the blue area?"
But in the ACF plot not a single lollipop is inside the blue area.
Any tips?
There are many different rules of thumb and everyone has own views. I would say, in your case you probably do not need the MA component at all. The rule with the lollipop refers to ACF/PACF plots that have a sharp cut-off after a certain lag, for example in your PACF after the second or third lag. Your ACF is trailing off which can be an indicator for not using the MA component. You do not have to necessarily use it and sometimes the data is not suited for an MA model. A good tip is to always check what pmdarima’s auto_arima() function returns for your data:
https://alkaline-ml.com/pmdarima/tips_and_tricks.html
https://alkaline-ml.com/pmdarima/modules/generated/pmdarima.arima.auto_arima.html
Looking at you autocorrelation plot you can clearly see the seasonality. Just because the ADF test tells you it is stationary does not mean it necessarily is. You should at least check if you model works better with seasonal differencing (D).
I have 20 years of data. I want to find the linear trend of the %s as a single number. EG if you were to plot the linear trend, there would be a coefficient by which the line increases/ decreases over time.
Google sheets has a trend function, but it's used for creating new data based on predicting trends.
Your question is too vague to answer clearly and precisely for what you want. Are you looking for the formula for the trend line? Just the correlation coefficient? Or a future value based on the info? The slope of the trend line?
What you have described is linear regression. I would suggest browsing the Insert drop down menu for formulas > statistics. There are formulas for each piece of info you want to draw (except creating the formula for you).
An easy and superficial way of obtaining the correlation coefficient and actual formula (and thus slope for linear trend lines), is to use excel. Copy your data table into excel and then create a scatterplot with the table. Go into the settings for the scatter plot and check the box for “trendline”. Then go into the trendline settings for the plot, and you can select which type of regression you want excel to use. You want linear. Towards the bottom of that menu, you want to check the boxes that say “show formula on chart” and “show R coefficient” or something along those lines. Excel will then print out your formula and coefficient in a text box on the chart. Your slope will be the coefficient of the x variable.
Hope this helps! Regression is a wormhole. I’d love to get more in depth if you’re interested!
NOTE: The outlier for year 2003 will have a significant impact on a linear regression line. Consider removing it from the data to create a line that will be more accurate for future predictions.
I have used ARIMA(0,1,0)(0,1,1)12 where seasonal lag is 12. The ACF plot & PACF plot of residuals suggests pattern where as box test for 12 lags, 24 lags etc shows p value in the range of 20% to 40% indicating randomness.
Is it really possible to have contradictory results OR there might be a problem in the way i modeled it.
I am using Arima function of R.
The original series has strong seasonality and upward trend.
Regards
Lakshmi