Time-Series Analysis

Correct Answer: Exponential smoothing assigns greater weight to more recent observations, allowing the model to adapt more quickly to changes in the underlying time series process.

The key advantage of using exponential smoothing over a simple moving average for forecasting a time series is that exponential smoothing assigns greater weight to more recent observations. This allows the model to adapt more quickly to changes in the underlying time series process. A simple moving average assigns equal weight to all observations within the specified window, which can lead to slower adaptation to changes in the time series. Exponential smoothing, on the other hand, gives more importance to recent data points, enabling the model to respond more rapidly to shifts in the data. The other two options are incorrect: Exponential smoothing generally requires fewer observations than simple moving averages to generate reliable forecasts, making it suitable for shorter time series as well. Exponential smoothing can account for trends and seasonal patterns by using variations such as double exponential smoothing (Holt's method) and triple exponential smoothing (Holt-Winters' method).

Correct Answer: Develop a momentum strategy that buys the stock after positive returns and sells after negative returns, seeking to profit from the tendency of returns to persist in the short term.

The most appropriate approach given the observed positive autocorrelation at lag 1 is to develop a momentum strategy. This strategy would buy the stock after positive returns and sell after negative returns, seeking to profit from the tendency of returns to persist in the short term. A mean reversion strategy would be more appropriate if the series exhibited negative autocorrelation, indicating that returns tend to revert to their long-run average over time. However, this is not the case in the given scenario. While conducting further analysis to determine if the autocorrelation is driven by common factors could provide additional insights, the presence of strong positive autocorrelation at lag 1 is sufficient information to suggest that a momentum strategy is likely to be effective in this case.

Correct Answer: Decomposition of the series into trend, seasonal, and irregular components

Decomposition of the series into trend, seasonal, and irregular components is the most appropriate technique for analyzing a time series that exhibits both trend and seasonality. This method allows for separating the time series into its individual components, making it easier to understand the underlying patterns and forecast future values. By isolating the trend and seasonal components, analysts can better assess the long-term direction and recurring patterns within the data. Fitting an ARIMA model to the original series data may not be the best approach, as ARIMA models are more suitable for capturing short-term dependencies and may struggle to accurately represent both trend and seasonality simultaneously. Applying a simple exponential smoothing model is not ideal, as it is designed to capture either trend or seasonality, but not both at the same time. To effectively model a time series with both trend and seasonality, more advanced techniques like decomposition or more sophisticated exponential smoothing methods (e.g., Holt-Winters) are required.