Components of time series
Name and elaborate the four components of time series in brief.
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• TREND (SECULAR TREND):Time series data would normally show an upward or downward trend over a period of time. A trend is a longterm movement in time series. They are generally gradual increases or decreases over a period of time and an example of an upward trend would be price increases over the years, and a downward trend would be decrease in sales over the years. The increase or decrease is fairly gradual and thus a smooth curve or straight line curve generally depicts the trend.
• CYCLICAL VARIATIONS (C):These variations are not regular as seasonal variation, they are medium to long term deviations from the trend. Cyclical variations are recurrent upward or downward movements in a time series but the period of cycle is greater than a year. There are different cycles of varying in length and size. A business cycle is one of the most common forms and passes through stages.
• SEASONAL VARIATIONS (S):Seasonal variations are fluctuations that are repeated periodically, they are short term fluctuations and occur periodically within a year. Major factors causing this repetition are weather conditions and customs of people.• RANDOM (IRREGULAR) VARIATION (R):
These are fluctuations in time series that are short in duration, unpredictable occurrences that are erratic in nature and follow no regular pattern. They result due to unforeseen events such as droughts, strikes etc.
Suppose we have a stick of length L. We break it once at some point X _ Q : Problem on Chebyshevs theorem 1. Prove 1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the
1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the
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Define the term Correlation and describe Correlation formula in brief.
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Define the term Frequency Distributions?
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