Sample autocorrelation at lag1, lag2, and lag 3 denoted by r1, r2, and r3 for large ‘n’ for weekly thermostat sales of one year are 0.4954 , 0.3285, and 0.0959. Assuming that SAC cuts of after lag3 and using level of significance = 0.05, the SAC provides the evidence that thermostat sales series: (a)stationary, (b)complies Box & Jenkins approach, (c) cuts off or (d) All of them
To determine whether the given sample autocorrelation at lag1, lag2, and lag3 provide evidence about the properties of the thermostat sales series, we need to analyze each option (a), (b), (c), and (d) separately.
(a) Stationary:
To test whether the time series is stationary based on the sample autocorrelations, we need to check if all autocorrelations decrease to zero or become insignificant after a certain lag. Since the given SAC cuts off after lag3, it suggests that the autocorrelations decrease and become insignificant after lag3. This indicates that the series is likely stationary.
(b) Complies Box & Jenkins approach:
The Box & Jenkins approach in time series analysis typically involves identifying the order of autoregressive (AR) and moving average (MA) models to fit the data. In this case, the information provided about the sample autocorrelations does not directly indicate whether the series complies with the Box & Jenkins approach. Further analysis, such as examining the partial autocorrelation function (PACF) and performing model fitting, is required to determine if the series is suitable for the Box & Jenkins approach.
(c) Cuts off:
The given information explicitly states that the SAC cuts off after lag3. This means that the autocorrelations become insignificant at lag4 and beyond. Therefore, we can conclude that the SAC indeed cuts off.
(d) All of them:
Based on the given information, we can conclude that option (d) is the correct answer. All of the properties mentioned in options (a), (b), and (c) seem to be supported by the SAC results.
In summary, according to the provided sample autocorrelations, the thermostat sales series is likely stationary, the SAC cuts off after lag3, and compliance with the Box & Jenkins approach would require further analysis beyond the given SAC information.