Step 1: Understanding the Concept:
Time series analysis breaks data down into four components: secular trend, seasonal variations, cyclical variations, and irregular variations. Measuring the 'trend' specifically involves isolating the long-term upward or downward movement of the data over time.
Step 2: Key Formula or Approach:
The commonly accepted techniques for measuring trend include:
1. Graphical Method: Visual inspection and sketching a freehand curve.
2. Method of Least Squares: Fitting a mathematical model (like a linear regression line) to the data to minimize the sum of squared errors.
3. Moving Averages Method: Averaging data points over a specific window to smooth out short-term fluctuations and highlight the trend.
Step 3: Detailed Explanation:
The "Method of cyclic component" is specifically used to identify and measure the rhythmic, periodic fluctuations in data that occur over periods longer than one year, which is distinct from the secular trend. Therefore, it is not a method for measuring the long-term trend itself.
Step 4: Final Answer:
The methods used for measuring trends are (A), (B), and (D).