# Help understanding ARIMA Model and ACF

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• semidevil
In summary, ARIMA is a useful tool for assessing and making stationary models with any set of data before making forecasts. To start, one should plot the ACF and PCF to check for correlation lags and trends. If there is a pattern, taking the first difference may be necessary, and if there is still a trend, considering the natural log may help. The objective is to have a random-looking ACF below the confidence shade. Seasonality can also be addressed by considering the seasonal component. The diff(log10) plot in this case does not look stationary and appears to be autocorrelated. As for the ACF and PCF, there may still be spikes above the blue line, indicating potential seasonality. More information on
semidevil
I've read a few resources on ARIMA, and I still have a few outstanding questions. Here is what I know, and let me know if I am incorrect:

Given any set of data, before I can do any forecast, I can use ARIMA to assess the model and make it stationary first.

Before I start, I should plot out the ACF and PCF. The ACF shows the correlation lags and also tells me if there is a trend. If my ACF starts high and gradually dies down, then I should take the first difference. I plot the ACF again and see if there is a pattern. If there is, that means my variance is not stationary. Then, I can consider taking the natural log. I plot the ACF of the differenced logs, and my objective is to have my ACF look "random" and below the confidence shade.

I might still see a spike every 12 months (for example), so that means there is a seasonality. In this case, I need to consider the seasonal component to it.Is this correct so far? I haven't mentioned PCF, because I still don't know what it represents. If someone can explain, that will be great.

Also, to give some context, I've attached some photos of my data: It includes the difference of the log10, and the ACF, PCF.

question:

for the diff(log10), would you say this is stationary? plotting the raw data, it was trended, taking the first difference it was still not stationary in the variance, so I took the diff(log10), which looked much better...but I still can't decide if this is stationary or not.

for the ACF and PCF:
Would you say there is seasonality, since there are still spikes above the blue line? How would you interpret this ACF and PACF in general?

same question with the PCF. what does this mean?

Your diff log10 plot does not look stationary. In particular variance seems to increase with time. Also it appears to be autocorrelated. Re pcf here is a source you might find useful: http://people.duke.edu/~rnau/411arim3.htm

## 1. What is an ARIMA model and how does it work?

An ARIMA (Autoregressive Integrated Moving Average) model is a popular statistical method used for forecasting time series data. It combines the concepts of autoregression (AR) and moving average (MA) to account for the trends and patterns in the data. The model uses past data to make predictions about future values by identifying relationships between data points and using that information to make forecasts.

## 2. What is the purpose of ACF in ARIMA modeling?

ACF (Autocorrelation Function) is a tool used to identify patterns and correlations in a time series data. It helps in determining the optimal order of the ARIMA model, which is crucial for accurate forecasting. The ACF plot shows the correlation between data points at different lags, helping to identify any significant patterns or trends in the data.

## 3. How do I interpret the ACF plot?

The ACF plot has two important features: the correlation coefficient and the confidence interval. The correlation coefficient represents the strength of the relationship between data points at a specific lag. The confidence interval shows the range within which the true correlation coefficient is likely to fall. If a correlation coefficient falls outside the confidence interval, it is considered statistically significant.

## 4. What is the difference between ACF and PACF in ARIMA modeling?

PACF (Partial Autocorrelation Function) is a measure of the correlation between a data point and its lagged values, after removing the effects of all shorter lags. In contrast, ACF measures the correlation between a data point and all of its previous lagged values. PACF is used to determine the optimal order of the AR component in an ARIMA model, while ACF is used to determine the optimal order of the MA component.

## 5. Can ARIMA models be used for non-stationary time series data?

Yes, ARIMA models can be used for non-stationary time series data. However, in such cases, the data needs to be transformed to make it stationary. This can be done by taking the difference between consecutive data points (differencing) or using other techniques like logarithmic transformations. Once the data is stationary, an ARIMA model can be applied to make accurate forecasts.

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