Financial Risk Manager Part 1
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What is the purpose of a q-th-order moving average process?
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TTanishq
A
To add a fifth error term to an MA(1) process.
B
To add a third error term to an MA(1) process.
C
To add as many additional lagged variables as needed so as to produce a robust set of estimates for the time series.
D
To invert the moving average representation and make it more useful.
Explanation:
Explanation
A q-th-order moving average process, denoted as MA(q), is used to model time series data where the current value depends on the current error term and q previous error terms.
Key points:
- An MA(q) process includes q lagged error terms, not just a fixed number like 3 or 5
- The purpose is to capture the dependency of the current observation on past random shocks
- By including additional lagged error terms, the model can better represent the autocorrelation structure of the time series
- This allows for more robust parameter estimation and better forecasting
Why other options are incorrect:
- A & B: These are too specific (fifth or third error term) - MA(q) can have any number q of lagged error terms
- D: Inversion is related to converting between AR and MA representations, not the primary purpose of MA(q)
Mathematical form of MA(q) process: [ Y_t = \mu + \varepsilon_t + \theta_1\varepsilon_{t-1} + \theta_2\varepsilon_{t-2} + \cdots + \theta_q\varepsilon_{t-q} ] where q represents the order of the moving average process.
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