Questions:

1. What are PACF and ACF for?

2. Which one is used for AR and MA, respectively?

3. What is residual?

Your answer:

1. ......

2. ......

3. ......

They both measure the correlation between a time series and its lagged values. But ACF shows how past values affect current values and PACF shows the direct influence of a lag after accounting for shorter lags after removing the effect of shorter lags.

2.

-PACF is used to identify the order of AR, as it shows the direct effect of a lag.

-ACF is used to determine the order of MA, as it shows the overall correlation between the current and lagged values.

3.

Residual is the error between actual value and predicted value. The model's error.

1. PACF and ACF used to identify the order of AR and MA models.

2. PACF is used to determine the number of AR terms (p) while ACF is used to determine the number of MA terms (q).

3. Residual is the difference between the actual value and the predicted value from a model. In time series, residuals represent the errors left after the model has explained the structure in the data.

2. ACF is used for MA(q)

   PACF is used for AR(p)

3. residual is differences in value between the actual and the predicted value.

• PACF (Partial Autocorrelation Function) and ACF (Autocorrelation Function) are used to analyze the correlation between current and past values in a time series. ACF shows the overall correlation with all previous lags, while PACF shows the direct correlation between the current value and a specific lag, excluding the effects of the intermediate lags.

• PACF is typically used to identify the appropriate number of lags for an AR (Auto-Regressive) model, while ACF is used to identify the lags for an MA (Moving Average) model.

• Residual refers to the difference between the actual observed value and the value predicted by the model. It represents the error or the part of the data not explained by the model. Ideally, residuals should look random and show no clear pattern if the model fits well.

1. ACF = Tells how the time series is correlated with its on past value at different time lags.

   PACF = Tells the correlation between the series and its lagged version, without indirect effects.

2. For AR, significant PACF is used, up to lag p then it is dropped.

   For MA, significant ACF is used, up to lag q then it is dropped.

3. Residual is the difference between actual and predicted value from the model.

1. ACF looks at the overall connection with previous days, while PACF focuses on the direct relationship with one specific past day, ignoring the one in between.

2. We use PACF to find out how many AR terms to include because it shows the direct effect of past values. We use ACF to decide the number of MA terms because it shows how past errors affect current values.

3. A residual is just the difference between what actually happened and what the model guessed would happen.

• ACF (Auto-Correlation Function)

  - the correlation bet observation at the current time spot and the observations at previous time spots

  - identifying MA order (q)

  
  

• PACF (Partial Auto-Correlation Function)

  - the correlation bet observations at 2 time spots given that we consider both observations are correlated to the day before yesterday, and yesterday can also be correlated to the day before yesterday

  - identifying AR order (p)

Question 2

• ACF - used for MA

• PACF - used for AR

Question 3

• Residual is the difference bet actual and predicted value

residual = actual value - predicted value

1. PACF and ACF are used to analyze the autocorrelation structure of time series data. They help us identify the correlation patterns between observations at different lag orders in the series, and then provide a basis for judging the characteristics of the time series (such as whether there is a trend or periodicity) and determining the appropriate order when building models like AR and MA.

2. PACF is used to determine the order of the AR (Autoregressive) model, and ACF is used to determine the order of the MA (Moving Average) model.

3. Residual is the difference between the actual observed value and the model - predicted value in a time - series (or other prediction) model. It represents the unexplained data fluctuations of the model and can be used to test the model’s fitting effect.

ACF shows overall correlation between current and lagged values.

2. PACF is used for identifying AR order.

ACF is used for identifying MA order.

3. Residual is the difference between actual and predicted values.

1. What are PACF and ACF for?

• ACF Measures the correlation between a time series and its lagged values.

• PACF Measures the correlation between a time series and its lagged values after removing the effects of shorter lags.

2. Which one is used for AR and MA, respectively?

• AR Use PACF to determine the number of lags.

• MA Use ACF to determine the number of lags.

3. What is residual?
A residual is the difference between the observed value and the predicted value from a model.

- Shows how current values are related to past values

PACF (Partial Autocorrelation Function)

-Checks the relationship with the past, but removes the effect of the middle steps.

2. -Use ACF to find the ‘MA’ (Moving Average) part of ARIMA.

MA model → Use ACF to find q.

- Use PACF to find the ‘AR’ (AutoRegressive) part of ARIMA.

AR model → Use PACF to find p.

3. Residual is the difference between the actual value and the predicted value in a model. It tells us how much the model's prediction missed the real data.

1. Both help identify patterns and guide model selection. ACF shows correlation between current value and its past values or lags. PACF shows correlation between current value and lagged values after removing effects of intermediate lags.

2. Use PACF to determine AR and ACF to determine MA.

3. Residuals tell how well the model fits the data. Good models have residuals that look like random noise.

ACF- Auto Correlation Funtion refers to the correlation between time series and its lagged version

PACF- Partial Auto Correlation Function refers to the correlation between time series and a lagged version of itself, controlling for the effects of jntermediate lags.

2)

ACF-Used for MA as it cuts off after lag q

PACF-Used for AR as it cut offs after lag p

3)

Residual is the difference between observed value and value predicted by time series model. The residuals helps to evaluate model accuracy (smaller residuals means better model), derect model problems (trends, seasonality or autocorrelation) and ensure randomness (good residuals like white noise).