based trend calculation

1. Time Based Trend
Calculation

2. Learning Objectives
• Correctly apply and explain the following tools:
- momentum
- rate of change
- moving average,
- accumulative average
- reset accumulate average
• Contrast the use of various moving averages
• Explain the drop-off effect
• Determine the strength of a trend based on indicator data
• Select the correct definition of trend strength indicators

3. Forecasting & Following
(a) There is a clear distinction between forecasting the trend and finding
the current trend.
(b) Forecasting, predicting the future price, is much more desirable but
very complex. It involves combining those data that are most important
to price change and assigning a value to each one. The results are
always expressed with a confidence level, the level of uncertainty in the
forecast.
(c) The techniques most commonly used for evaluating the direction or
tendency of prices both within prior ranges or at new levels are called
autoregressive functions.
(d) Unlike forecasting models, they are only concerned with evaluating the
current price direction. This analysis concludes that prices are moving in an
upward, downward, or sideways direction, with no indication of
confidence. From this simple basis, it is possible to form rules of action and
develop complex trading strategies.

4. Forecasting Methods
Auto Regressive
Model
Least Squares
Model
Error Analysis

5. Auto Regressive Model
• A statistical model is autoregressive if it predicts future values based on
past values. For example, an autoregressive model might seek to predict a
stock's future prices based on its past performance.
• Autoregressive models predict future values based on past values.
• They are widely used in technical analysis to forecast future security
prices.
• Autoregressive models implicitly assume that the future will resemble the
past.
• Therefore, they can prove inaccurate under certain market conditions,
such as financial crises or periods of rapid technological change.
• Multiple regression models forecast a variable using a linear combination
of predictors, whereas autoregressive models use a combination of past
values of the variable.

6. Least Squares Model
• The least squares method is a statistical procedure to find the best fit for
a set of data points by minimizing the sum of the offsets or residuals of
points from the plotted curve.
• Least squares regression is used to predict the behavior of dependent
variables.
• An example of the least squares method is an analyst who wishes to test
the relationship between a company’s stock returns, and the returns of
the index for which the stock is a component. In this example, the analyst
seeks to test the dependence of the stock returns on the index returns. To
achieve this, all of the returns are plotted on a chart. The index returns
are then designated as the independent variable, and the stock returns
are the dependent variable. The line of best fit provides the analyst with
coefficients explaining the level of dependence.

7. Error Analysis Model
• A simple error analysis can be used to show how time works against the
predictive qualities of regression, or any forecasting method.
• The forecast error is the difference between the projected price and the
actual price.
• The standard deviations of the five forecast errors , taken over the entire
10 years, shows the error increasing as the days-ahead increase.
• This confirms the expectation that forecasting accuracy decreases with
time and that confidence bands will get wider with time.
• For this reason, any forecasts used in strategies will be 1-day ahead.

8. Trend Calculation Method
Momentum
(Price change
over Time)
The Moving
Average
Accumulative
Average
Reset
Accumulative
Average
Drop Off Effect

9. Momentum (Price change over Time)
• The most basic of all trend indicators is the change of price over some period
of time.
• If the change in price is positive, we can say that the trend is up, and if negative,
the trend is down.
• Momentum is the rate of acceleration of a security's price or volume—that is,
the speed at which the price is changing.
• Simply put, it refers to the rate of change on price movements for a particular
asset and is usually defined as a rate.
• In technical analysis, momentum is considered an oscillator and is used to help
identify trends.
• Investors can use momentum as a trading technique.
• Once a momentum trader sees acceleration in a stock's price, earnings or
revenues, the trader will often take a long or short position in the stock in the
hope that its momentum will continue in either an upward or downward
direction.
• This strategy relies on short-term movements in a stock's price

10. Moving Averages
• The most well-known of all smoothing techniques, used to remove
market noise and find the direction of prices, is the moving average (MA).
• Using this method, the number of elements to be averaged remains the
same, but the time interval advances.
• This is also referred to as a rolling calculation period.
• The length of a moving average can be tailored to specific needs.
• A 63-day moving average, 1/4 of 252 business days in the year, would
reflect quarterly changes in stock price, minimizing the significance of
price fluctuations within a calendar quarter.
• The stock market has adopted the 200-day moving average as its
benchmark for direction; however, traders find this much too slow for
timing buy and sell signals.

11. Accumulative Averages
• An accumulative average is simply the long-term average of all data, but it
is not practical for trend following.
• One drawback is that the final value is dependent upon the start date.
• If the data have varied around the same price for the entire data series,
then the result would be good.
• It would also be useful if you are looking for the average of a ratio over a
long period.
• Experience shows that price levels have changed because of inflation or a
structural shift in supply and/or demand, and that progressive values fit
the situation best.

12. Reset Accumulative Averages
•A reset accumulative average is a modification of the
accumulative average and attempts to correct for the loss
of sensitivity as the number of trading days becomes
large.
•This alternative allows you to reset or restart the average
whenever a new trend begins, a significant event occurs,
or at some specified time interval,
• for example, at the time of quarterly earnings reports or
at the end of the current crop year.

13. Drop Off Effect
• Simple moving averages, linear regressions, and
weighted averages all use a fixed period, or window, and
are subject to this. For an n-period moving average, the
importance of the oldest value being dropped off is
measured by the difference between the new price being
added to the calculation
•A front-weighted average, in which the oldest values
have less importance, reduces this effect because older,
high volatility data slowly become a smaller part of the
result before being dropped off.
•Exponential smoothing, discussed next, is by nature a
front-loaded trend that minimizes the drop-off effect as
does the average-off method.