in:

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  Closing price of stock j on the kth trading day of month t. The value range of k is [d-L+1, d], where d is the last trading day of the month.

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  The window width of the moving average is the time span used to calculate the moving average, such as 5 days, 10 days, 20 days, etc. Different L values ​​represent different time scales.

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  The moving average price of stock j in month t with a window width of L. It reflects the average level of stock prices within a specific time window.

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  Standardized moving average price. By dividing the moving average price by the closing price on the last trading day of the month, the difference in the absolute value of different stock prices is eliminated, making the moving averages of different stocks comparable.

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  The rate of return of stock j in period t. This generally refers to the monthly rate of return, calculated as $r_{j,t} = (P_{j,d}^{t} - P_{j,d-1}^{t})/ P_{j,d-1}^{t}$ .

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  In period t, the factor return (or factor loading) of the standardized moving average price $M\bar{A}_{j,t-1,L_i}$ of the i-th time window $L_i$ estimated by the regression model. It represents the contribution of the momentum signal of this time window to the stock return.

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  The error term in the regression model reflects the part of the return that the model cannot explain.

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  Based on the average of the factor returns over the past 12 months, the expected value of the factor return for the next month is obtained. Using the average of the factor returns over the past period as an estimate of the future factor returns takes advantage of the mean reversion characteristics of the factor returns.

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  Based on the moving average of each time window and the expected factor return, the expected return of stock j in the next period (t+1) is calculated. It comprehensively considers the impact of momentum signals on future returns at different time scales.