Financial Risk Manager Part 1
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Consider the following statements regarding an autoregressive moving average (ARMA) process:
I. The process combines the lagged unobservable random shock characteristic of the MA process with the observed lagged time series characteristic of the AR process II. The process involves gradually-decaying autocorrelations
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NNikitesh
A
Only I is correct
B
Only II is correct
C
Both I and II are correct
D
Both I and II are incorrect
Explanation:
Explanation:
Statement I: This statement is correct. An ARMA (Autoregressive Moving Average) process indeed combines two components:
- AR (Autoregressive) component: Uses lagged values of the time series itself (observed lagged time series)
- MA (Moving Average) component: Uses lagged values of the random error terms (lagged unobservable random shocks)
Statement II: This statement is also correct. ARMA processes typically exhibit gradually-decaying autocorrelations. The autocorrelation function (ACF) of an ARMA process decays gradually rather than cutting off abruptly, which is a characteristic feature that distinguishes ARMA processes from pure AR or MA processes.
Key Points:
- ARMA(p,q) models combine AR(p) and MA(q) components
- They are more flexible than pure AR or MA models
- The ACF pattern helps identify ARMA processes in time series analysis
- Both statements accurately describe fundamental characteristics of ARMA processes
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