Final answer:
No, you cannot directly apply quarterly time-series data with a trend to models assuming stationary data without first detrending the data or using models that account for such trends.
Step-by-step explanation:
No, quarterly time-series data with a trend cannot be directly applied to models that assume stationary data. Time-series data exhibiting a trend is known as nonstationary because its statistical properties, like the mean and variance, change over time. To use this type of data in models that require stationary data, one must first 'detrend' the data or use modeling techniques that account for trends, such as differencing or using a nonlinear model. These adjustments can help to stabilize the mean of the series over time, allowing for the use of stationary models.
Stationarity is a key assumption in many time-series models because it ensures that the properties of the series do not depend on the time at which the series is observed. If trends are present, they can lead to erroneous conclusions about relationships and forecasts.
The utility of regression analysis in predicting sales (as seen in the prediction exercise for the electronics retailer) may be affected if underlying assumptions including stationarity are not met or not properly accounted for before applying the model.