Final answer:
The statement that time-series models are used to forecast future movements of a variable based on the past behavior of the variable is true. These models analyze historical data patterns to predict future events, but their effectiveness may diminish if past patterns don't recur. Time series graphs assist in visualizing data trends to support these predictive models.
Option 'a' is the correct.
Step-by-step explanation:
The statement 'Time-series models are used to explain and forecast the future movements of a variable based on the past behavior of the variable' is true. Time-series models are, indeed, statistical tools that analyze sequences of data points, collected over time intervals, to forecast future events. These models assume that past patterns observed in the data are likely to continue into the future, which is a fundamental concept in time-series analysis.
For example, in a given statistical model, such as the fluctuating temperature of a refrigerator, the time series of temperature readings could be used to predict future temperature fluctuations, based on the pattern of when the compressor turns on or off. Similarly, manufacturers use time-series analysis to monitor and control the fill weight of a product like a bag of rice, aiming to minimize variance and ensure consistency. Time-series analysis is valuable across various fields, including economics, finance, meteorology, and engineering, wherein forecasting future trends based on historical data is crucial for decision-making processes.
However, while time-series models are incredibly useful in foreseeing future scenarios, they do have limitations. They depend on the assumption that historical patterns will recur, which may not always hold true in the presence of structural changes or new, unprecedented events. As such, models may need to be adapted or replaced over time to maintain predictive accuracy.
The use of time series graphs can make it easier to visualize trends, patterns, and anomalies in data over time, thus aiding in the construction of effective models. Decision-makers in business and government often rely on these models to guide strategic planning and responses to predicted changes.