University Statistics Exam Questions on Time Series Trend and Pattern Analysis

📚 Quick Study Guide

• 📈 Time Series: A sequence of data points indexed in time order.
• ⏱️ Trend: Long-term movement in a time series. Can be linear, exponential, or polynomial.
• seasonality_check ☀️ Seasonality: Regular, predictable fluctuations that occur within a year.
• cyclical_graph 🔄 Cyclical Patterns: Fluctuations that occur over longer periods, typically more than a year.
• ➕ Additive Model: Time series = Trend + Seasonality + Random Variation ($Y_t = T_t + S_t + R_t$).
• ✖️ Multiplicative Model: Time series = Trend × Seasonality × Random Variation ($Y_t = T_t \times S_t \times R_t$).
• 📏 Moving Average: A technique to smooth out short-term fluctuations and highlight longer-term trends.
• 🧪 Exponential Smoothing: Assigns exponentially decreasing weights to past observations.

Practice Quiz

1. Which component of a time series represents long-term movements in the data?
   1. A) Seasonality
   2. B) Cyclical Variation
   3. C) Trend
   4. D) Random Variation
2. What type of model assumes that the components of a time series add together?
   1. A) Multiplicative Model
   2. B) Additive Model
   3. C) Exponential Model
   4. D) Logarithmic Model
3. Which method is used to smooth out short-term fluctuations in a time series?
   1. A) Regression Analysis
   2. B) Moving Average
   3. C) Correlation Analysis
   4. D) Hypothesis Testing
4. Seasonality in a time series refers to:
   1. A) Long-term trends
   2. B) Irregular fluctuations
   3. C) Regular, predictable fluctuations within a year
   4. D) Cyclical patterns over many years
5. In the additive model, if the trend is 50 and the seasonality is 10, what is the expected value, ignoring random variation?
   1. A) 5
   2. B) 60
   3. C) 40
   4. D) 500
6. Which smoothing method assigns exponentially decreasing weights to past observations?
   1. A) Simple Moving Average
   2. B) Weighted Moving Average
   3. C) Exponential Smoothing
   4. D) Linear Regression
7. What is the primary difference between cyclical and seasonal patterns in time series?
   1. A) Cyclical patterns are predictable, while seasonal patterns are not.
   2. B) Seasonal patterns occur over longer periods than cyclical patterns.
   3. C) Cyclical patterns occur over longer periods than seasonal patterns.
   4. D) There is no difference between them.