Linear Regression

Linear regression is a statistical tool used to predict future prices based on historical data, and is usually used to determine when prices are overheated. Use the method of least squares to build "the best" straight line through a number of price points. Price points, used as input data can be any of the following values: open, close, maximum, minimum, (maximum + minimum) / 2, (maximum + minimum + close) / 3 (opening + maximum + minimum + closure ) / 4,% change, or (open + close) / 2. These data can be pre arbitrarily narrowed to building the most appropriate line. If smoothing is not desirable, then simply choose the smoothing period equal to 1.

Calculation
To determine the best line, corresponding to a number of price points, using the method of least squares.
The standard deviation is calculated as follows:
- Summed squares of the difference between the price and the line of linear regression.
- Porluchennaya sum is divided by the number of bars in the range of the regression series.
- Calculated the square root of the result, which gives the standard deviation.

To illustrate the above presented daily schedule of Japanese candles "DKWD" (D & K Healthcare Resources). The blue line represents the central line of regression, based on the parameters selected below. The red lines represent the channel, based on standard deviations, set the example below.

The use of graphics programs
. Price - the price set by the value (opening, closing.) That are used as input data for calculating the regression line.
. Type of pre-smoothing. - The type of smoothing (simple, exponential.) Used for pre-smoothing the data before performing the regression.
. Pre-smoothing. - Smoothing period used for the pre-smoothing the data before performing the regression.
. The range of data - this group of plants contains parameters that define the beginning and end of analysis.
. Automatic use of the past X bars - this option provides for automatic movement of the regression line, always using the last X bars.
. From dd / mm / yy hh: mm: ss to dd / mm / yy hh: mm: ss - This option allows the user to define a specific start point and end point of time.
. From dd / mm / yy hh: mm: ss to Present - This option allows you to automatically move the regression line, always starting with a certain fixed start-bar, and always finish at the last bar. The range will be expanded, as is expanding the time period.
. The standard deviation up - the number of standard deviations above the regression line to make a parallel line of the channel (if 0 - line missing). You can specify multiple levels of the channel in this parameter, a comma separating the values (eg, 1, 1.5, 2).
. Standard ot.lonenie down - the number of standard deviations below the regression line to make a parallel line of the channel (if 0 - line has not done). Here you can also specify several levels of the channel, just a comma separating the values (eg, 1, 1.5, 2).
. Channels Raffi - developed by Hilbert Raffo, this method is the maximum distance between any price and the closing line of regression. This distance is then used as the basis for the channels. Channels conducted parallel regression lines, above and below the line at a distance equal to the maximum calculated distance. The upper channel is then used as a resistance, but lower as a support.
. Continue to the right - this option allows you to continue the line of regression (and through the channel, if applicable) to the right of the chart.
. Color regression - sets the color and style of the regression line on the graph.
. Color Channel - sets the color and style of the line feed on the graph.

Description of parameters
There are several options for choosing the price range that will be included in the regression analysis (range data). The first option "Automatically use the last X bars" allows you to automatically move the regression line, always use the most recent X bars. The second option is "from dd / mm / yy hh: mm: ss to dd / mm / yy hh: mm: ss", allows the user to define specific start and end point of your time. The third option is "from dd / mm / yy hh: mm: ss, to date" is the other possibility of automatic displacement of the regression line, always starting in a certain defined start bar, and always ending in the most recent bar. The range of data will grow, since growing period of time.

Some software products allow to build a linear regression by hand, for this set of tools just click the relevant icon (for example), and activates a tool for constructing a linear regression. Then the mouse cursor indicates the point on the graph, which must start a line of regression and a manual line between two points of interest. Along with the regression line can be straight lines strips parallel to the regression line. The stripes are on the user-specified distance above and below the regression line. Distance determined by the number of standard deviations from the regression line. The user is not limited to building only one line of the channel above and below the line of linear regression, because you can define several levels, simply list them separated by commas. For example, you can:

Standard deviation upwards: 1, 1.5, 2
The standard deviation below: 1, 1.5, 2

In this case, will be constructed in three channels at 1, 1.5, and 2 standard deviations from the regression line, respectively. The value of standard deviation is calculated using the same range of data that is used in determining the regression line (range data). The values specified in the parameters are the multiplier of the value of standard deviation used to calculate the distance from the channel of the regression line.

If the option Feeds Raffi will be used a different method to calculate the bands. The resulting Hilbert Raffo, this method is the maximum distance between any price and the closing line of regression. This distance is then used as the basis for the channels. Channels are parallel to the regression line above and below it at a distance equal to the maximum calculated distance. The upper channel is then used as a resistance, while the lower channel is used as support. You can also ask a number of levels, separated by commas. Levels will be used as factors in the standard channel Raffi. To simply hold a standard channel Raffo, define a multiplier of 1 for the upper and the lower channel.

Linear regression can be arbitrarily extended to the right, using the "Extension of the line for the moment." This allows you to design the line to the right edge of the schedule. Start and end points of trend line is clearly visible as a small point on the line. These points can drag to a new position at the price chart. When the transfer occurs, re-compute the regression, and a new regression line with the new range of data. If you are using a range of data with the use of options "from dd / mm / yy hh: mm: ss for the moment, (Present)", then you can transfer only the starting point for a new fixed location. Start point then remain fixed, while the end-point adjust to the most recent bar.

The following approximations offer a few rules for the use of standard deviation units:

. Plus or minus one standard deviation covers 68.3% of the expected results (price movements)
. Plus or minus two standard deviations encompasses 95.4% of the expected results (price movements)
. Plus or minus three standard deviations includes 99.7% of the expected results (price movements)

For example, the movement of prices of more than 2 standard deviations above or below the regression line is quite rare (less than 5% probability). Such movements are usually treated as a state of perekuplennosti or pereprodannosti.

Strategies to use

To better understand the practical application of linear regression, the following are the comments of existing trederov who uses this tool in their daily practice.

Trader John Meyer
As a professional trader, I try to simplify their schedules and to use only those indicators that are simple and make sense. Channels of linear regression is best suited for this. If you are an advanced trader in the options market, you know the standard deviation.

I apply the indicator, based on the "Automatically use the last 100 bars." Graphs with a more prolonged period (more than 65 minutes), I have three channels of regression from a distance of 2, 3 and 4 standard deviations (in a different color). If you have azhiotazhnye buying or panic selling, the price could reach the area by 5 standard deviations, so be careful before you automatically go against the movement of the level of 2 standard deviations. If in doubt, go for a larger temporary format.

In the quiet days when the trade is carried out in a narrow price range, I am doing the installation of 1.2 standard deviations, and traded on a 3-minute charts - it usually gives at least ten transactions per day to obtain at least a small profit on each transaction.

Also, I see the location of the price of a certain distance of the standard deviations in different time formats. This approach gives me the perfect opportunity (for example: when a growing share is at a distance of 3 standard deviations on a weekly schedule - this is a golden opportunity for sale - while the majority of traders are still buying).

Channels linear regression, of course, is not some miraculous display, but with a good understanding of how it works, and its proper use, it can help a trader on the correct side of the market!

Trader Dan Clark
I use the 6 channels of automatic linear regression on their day and intra-day schedules (all time-formats). In fact, this two-line linear regression with a different number of bars and pre-smoothing. The first uses the last 55 bars (pre-smoothing 3), while the second uses the latest 233 bar (pre-smoothing 13). All use the method of least squares from the closing price. Thus, a regression of the 55 bars and one of 233 bars, each of channels 1, 2 and 3 standard deviations (total 6).

Channels linear regression very well serve to identify points perekuplennosti and pereprodannosti and breakthroughs. Pay attention to the behavior of "EMLX" February 14, when it breached its minimum of 1-channel standard deviation. February 15, the maximum of the day he returned and touched the same line of the channel, and then declined. 20 February, the daily minimum is close to 3-th channel, the standard deviation and pushed upwards. Pay attention to the pink line - 200-day EMA, which provides additional support.

Another reason why I prefer the channels of linear regression is that they help me escape from the traditional horizontal and vertical axes, and help me determine the direction of trend. For example, in the case of the "EMLX", although we have the perfect formation "double bottom", I think the breakthrough 1-th channel, the standard deviation would be a good opportunity to trade in the short side.

Trader Michael Walker.
I use linear regression in combination with stripes Bollindzhera (both LEDs at 2 standard deviations) to identify the peaks and the grounds.

50 bar automatic 1 pre-smoothing at 2 minute schedule of S & P 500. When the price band Bollindzhera channels and regression are found all together at the top or on the basis of the schedule and price, according to the oscillator is in a state of perekuplennosti or pereprodannosti (unless this trend day), then it is time to sell or buy.

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