a trading strategy based on Elliott Wave Theory - page 125

 
the scatter of the random variable (price) from the approximating model (desired function) cannot be smaller than the scatter of the random variable itself (sum of squares of Close[i]-Close[i+1])

"cannot be less" - is this already the criterion itself ? Or is it just a statement of the theorem ?

The point is that, as far as I understand it, it is not applicable in this case. The criterion can be used to find an order of polynomial which is sufficient for the approximating curve. But this curve will approximate the trajectory. Can you imagine an order of polynomial that would replicate in a smoothed form the behaviour of the trajectory?
 
In simple terms, did you call for a fitting?
 
Did you call for a simple fitting?

:-)
 
A book which is fully in line with the topic of the branch (solution finding). In addition to statistics problems there are examples of calculations in Excel, Mathcad and Statistica.
I did not find any in the mega list.

 
Yes, I also found it on Amazon - http://www.ozon.ru/context/detail/id/1908057/
 
Yes, I also found it on Amazon - http://www.ozon.ru/context/detail/id/1908057/

Rosh, could you scan the table of contents? I'd love to see it. It would take a long time to get it sent through Ozone. But perhaps you could do a review of the book in the near future. That is, what do you think would be useful?
 
Made an archive of 10 unprocessed photos, but it was too big (over 6 MB), so I'll probably post it later. I did process one page on this topic though:

 
Saved pictures (9 pages of content) in 2 archives, total 1100 kB

https://c.mql5.com/mql4/forum/2006/08/soderz.zip
from 1 to 5

https://c.mql5.com/mql4/forum/2006/08/soderz2.zip
from 6 to 9
 
I found an EA that trades with regression channels (that's what it says) from 20.04.05
I am using MQL-II, but maybe someone may need it. The author is not listed, I don't remember where I got it.

/*[[
VC-1hr
Lots := 0.1
Notes := Use in H1 timeframe.
Update on every tick := Yes
Enable Alerts := Yes
Disable alert once hit := No
Lots := 1
Stop Loss := 999
Take Profit := 200
Trailing Stop := 999
]]*/


// ====================================================================================================
// DECLARATION AND ASSIGNMENT
// ====================================================================================================

defines: Risk(1),mm(1),maxTradesPerPair(1);
Inputs : NumberName(1), iPeriod(21), MAShoot(50), DrawVertical(0), DrawText(0), ShowMA(0), LineWeight(1), BarsCount(0);
vars: spread(0),
Slippage(5),
sl(0),tp(0),
mode(0),
lastHigh(0),lastLow(0),lastOpen(0),lastClose(0),
target(0),
entryTS(0),
cnt(0),
first(0),
lotMM(0),
tHour(0),
CurrentTrades(0),
AccountIsMini(False);  // See comments near assignment statement below.

Var : shift(0), n_begin(0), n_end(0), n(0), a_(0), b_(0), a1(0), a2(0), a3(0), b1(0);
var : y1(0), y2(0), price(0), BarBegin(100), BarEnd(1);
var : tmp_div_high(0), tmp_div_low(0), stddiv_low(0),  stddiv_high(0), tmp_div(0);
var : x_n_up(0), x_n_down(0), x_1_up(0), x_1_down(0);
var : check_upper_chanel(false), color_1(0), color_2(0), name(""), angle(0), ratio(0), ratio_currency(0);
Var : MA(0), value(0), Bars_(170), check_low(false), check_high(false);
Var : save_low(0), save_high(0), save_shift_low(0), save_shift_high(0), save_shift(0);
Var : MAType(0), MAPrice(0);

//================================================================================================================
SetLoopCount(0);
comment("Auto Regression channel");

if BarsCount < 1 then Bars_ = Bars
else Bars_ = BarsCount;

save_low = -1;
save_high = -1;
save_shift_low = -1;
save_shift_high = -1;

check_low = false;	
check_high = false;	

MAType = MODE_SMA;
MAPrice = PRICE_CLOSE;

if Close[1] > 80 then ratio_currency = 100
else ratio_currency = 10000;

For shift = Bars_-1 Downto 0 Begin
	MA = iMAEx(iPeriod, MAType, 0, MAPrice, shift);
	
	if ShowMA then SetIndexValue(shift, MA);
	
	if MA - MAShoot/ratio_currency > Close[shift] then
	{
			
		if Close[Shift] < save_low or save_low = -1  then
		{
			check_low = true;
					
			save_low = close[Shift];
			save_shift_low = shift;
		};		
	};
	
	if MA  +  MAShoot/ratio_currency< Close[shift] then
	{
		if save_high < Close[Shift] or save_high = -1 then
		{
			check_high = true;	
			
			save_high = close[Shift];
			save_shift_high = shift;
		};
	};

	if check_low then
	{	
		if MA + MAShoot/ratio_currency < Close[shift] then 
		{
			check_low = false;	
			save_low = -1;
		};
	};
	
	if check_high then
	{
		if MA - MAShoot/ratio_currency > Close[shift] then 
		{						
			check_high = false;	
			save_high = -1;
		};
	};
	
End;

if save_shift_low > save_shift_high then
{
	n_begin = save_shift_low;
	n_end = save_shift_high;
}
else
{
	n_begin = save_shift_high;
	n_end = save_shift_low;
};

if n_end = 0 then n_end = 1; 
n = (n_begin - n_end + 1); 

a1 = 0;
a2 = 0;
a3 = 0;
b1 = 0;
a_ = 0;
b_ = 0;
y1 = 0;
y2 = 0;
tmp_div_high = 0;
tmp_div_low = 0;
tmp_div = 0;

if close[n_begin] < close[n_end] then check_upper_chanel = true
else check_upper_chanel = false;

For shift = n_begin Downto n_end Begin
	if check_upper_chanel then price = low[shift]
	else price = high[shift];
	
	a1 = a1 + shift*price;
	a2 = a2 + shift;
	a3 = a3 + price;
	b1 = b1 + shift*shift;
End;

b_ = (n*a1 - a2*a3)/(n*b1 - a2*a2);
a_ = (a3 - b_*a2)/n;
y1 = a_ + b_*n_begin;
y2 = a_ + b_*n_end;

MoveObject(	"Regression_middle" + NumberName, OBJ_TRENDLINE, Time[n_begin], y1, Time[n_end], y2, yellow, LineWeight, STYLE_SOLID);	

For shift = n_begin Downto n_end Begin
	if check_upper_chanel then price = low[shift]
	else price = high[shift];
	
	tmp_div = tmp_div + (price - (a_ + b_*shift))*(price - (a_ + b_*shift));	
End;	

stddiv_low = sqrt(tmp_div/n);
stddiv_high = sqrt(tmp_div/n);

x_n_up = y1 + 2*stddiv_high;
x_1_up = y2 + 2*stddiv_high;

x_n_down = y1 - 2*stddiv_low;
x_1_down = y2 - 2*stddiv_low;

if check_upper_chanel then  {
	color_1 = blue;
	color_2 = red;
}else{
	color_1 = red;
	color_2 = blue;
};
	
//upper
MoveObject(	"Regression_upper" + NumberName, OBJ_TRENDLINE, Time[n_begin], x_n_up, Time[n_end], x_1_up, color_1, LineWeight, STYLE_SOLID);	
//lower
MoveObject(	"Regression_lower" + NumberName, OBJ_TRENDLINE, Time[n_begin], x_n_down, Time[n_end], x_1_down, color_2, LineWeight, STYLE_SOLID);	

if  DrawText then
{	
	name = "Regression_bars_begin" + NumberName;
	MoveObject(name, OBJ_TEXT, Time[n_begin], x_n_down, Time[n_begin], x_n_down, red, 1, STYLE_SOLID);			
	SetObjectText(name, NumberToStr(n_begin,0), "System", 10, White);	
		
	name = "Regression_bars_end" + NumberName;
	MoveObject(name, OBJ_TEXT, Time[n_end], x_1_up, Time[n_end], x_1_up, red, 1, STYLE_SOLID);			
	SetObjectText(name, NumberToStr(n_end,0), "System", 10, White);	
}else{
	DelObject("Regression_bars_end" + NumberName, 0, 0, 0, 0);
	DelObject("Regression_bars_begin" + NumberName, 0, 0, 0, 0);
}

if DrawVertical then
{
	MoveObject(	"Regressin_begin" + NumberName, OBJ_VLINE, 	Time[n_begin], y1, Time[n_begin], y2, 	silver, 1, STYLE_DOT);	
	MoveObject(	"Regressin_end" + NumberName, OBJ_VLINE, 	Time[n_end], y1, Time[n_end], y2, 	silver, 1, STYLE_DOT);	
}else{
	DelObject("Regressin_begin" + NumberName, 0, 0, 0, 0);
	DelObject("Regressin_end" + NumberName, 0, 0, 0, 0);
}

//================================================================================================================


entryTS   = 4 * Point;          // Entry trailing stop - points
target    = TakeProfit * Point; // Profit target - points
lastHigh  = High[1];            // Last bar high
lastLow   = Low[1];             // Last bar low
lastOpen  = Open[1];            // Last bar open
lastClose = Close[1];           // Last bar close
spread    = Ask - Bid;          // Spread



// ====================================================================================================
// VALIDATION
// ====================================================================================================

if CurTime - LastTradeTime < 300 Then Exit;
if Bars < 100 or TakeProfit < 10 then Exit;
if IsIndirect(Symbol) = True then Exit;

if TrailingStop < 5 then
{
  print("invalid Trailing Stop");
  Exit;
};

// ====================================================================================================
// DATE CHOKE - For testing purposes
// ====================================================================================================
if TimeYear(time[0]) < 2004 then Exit;

// ====================================================================================================
// PYRAMIDING - LINEAR
// Money management risk exposure compounding
// ====================================================================================================

AccountIsMini = False; // Change to False for real trading w/ 100k/regular account
                       //        or for all backtesting, since backtests allow
                       //        fractional lots.
                       // Change to True for real trading w/ mini account

if mm <> 0 then 
{
  lotMM = Ceil(Balance * risk / 10000) / 10;

  if lotMM < 0.1 then lotMM = lots;

  if lotMM > 1 then lotMM = Ceil(lotMM);

  if AccountIsMini then lotMM = lotMM * 10;

  if lotMM > 100 then lotMM = 100;
}
else {
  lotMM = Lots; // Change mm to 0 if you want the Lots parameter to be in effect
};

// ====================================================================================================
// OPEN ORDER CHECK -
// Each instance of a script is attached to one currency pair.
// When this check executes, it sets CurrentTrades to 1 so that
// only one trade for this symbol will be open, which is enforced
// by "if CurrentTrades = 0".
// ====================================================================================================

CurrentTrades = 0;

for cnt = 1 to TotalTrades
{ 
  if OrderValue(cnt,VAL_SYMBOL) = Symbol then
  {
    CurrentTrades = CurrentTrades + 1; 
  };
};

// ====================================================================================================
// TRADE ENTRY
// ====================================================================================================

if CurrentTrades < maxTradesPerPair then
{
  //LONG TRADES ENTRY CRITERIA

  if //lastOpen < lastClose        and  // Last bar bullish, open less than close;
     check_upper_chanel = true   and  // Ask above lastHigh, and SAR less than Ask,
     y2 > Close     and  // then request order.
     tHour != TimeHour(time[0])  then
  {
    tHour=TimeMinute(time[0]);

    // Set stoploss to last bar low so that Bid must hit lastLow to exit.

    sl = x_1_down - (2 * point);
    tp = Ask + target;
  
    SetOrder(OP_BUY,
             lotMM,
             Bid,
             Slippage,
             sl,
             tp,
             LIME);
    Exit;
  };

  //SHORT TRADES ENTRY CRITERIA

  if //lastOpen > lastClose       and  // Last bar bearish, open greater than close;
     check_upper_chanel = False and  // if Bid below lastLow, and SAR greater than Bid,
     y2  < Close  and // then request order.
     tHour != TimeHour(time[0]) then
  {
    tHour=TimeMinute(time[0]);

    // Set stoploss to last bar high so that Ask must hit lastHigh to exit.

    sl = x_1_up + (2 * point);
    tp = Bid - target;

    SetOrder(OP_SELL,
             lotMM,
             Ask,
             Slippage,
             sl,
             tp,
             RED);
    Exit;
  }; 
}; // end of if CurrentTrades < maxTradesPerPair

// ====================================================================================================
// TRAILING STOP UPDATE
// ====================================================================================================

if CurrentTrades = 0 then exit;

for cnt = 1 to TotalTrades
{ 
  if OrderValue(cnt,VAL_SYMBOL) = Symbol then 
  {
    if OrderValue(cnt,VAL_TYPE) = OP_BUY then 
    {
      // If Bid - Open is now higher than entryTS pips profit,
      // and the stop loss order is lower than
      // entryTS pips below the Bid, then adjust the stop loss part of
      // the order to the Bid - entryTS pips

      if (Bid - OrderValue(cnt,VAL_OPENPRICE)) > (entryTS) then
      {
        if OrderValue(cnt,VAL_STOPLOSS) < x_1_down then
        {
          ModifyOrder(OrderValue(cnt,VAL_TICKET),
                      OrderValue(cnt,VAL_OPENPRICE),
                      x_1_down - (2 * point),
                      OrderValue(cnt,VAL_TAKEPROFIT),
                      BLUE);
          Exit;
        }; 
      };
      
      // if Stop Loss > Open Price then Set Takeprofit 

      if OrderValue(cnt,VAL_STOPLOSS) >= OrderValue(cnt,VAL_OPENPRICE) then
      {
        ModifyOrder(OrderValue(cnt,VAL_TICKET),
                    OrderValue(cnt,VAL_OPENPRICE),
                    OrderValue(cnt,VAL_STOPLOSS),
                    Ask + TakeProfit * Point,
                    BLUE);
        Exit;
      };
    }; // end OP_BUY check

    if OrderValue(cnt,VAL_TYPE) = OP_SELL then
    {
      // If Open - Ask is now higher than entryTS pips profit,
      // and the stop loss order is higher than
      // entryTS pips above the Ask, then adjust the stop loss part of
      // the order to Ask + entryTS pips

      if (OrderValue(cnt,VAL_OPENPRICE) - Ask) > (entryTS) then
      {
        if OrderValue(cnt,VAL_STOPLOSS) > x_1_up then
        {
          ModifyOrder(OrderValue(cnt,VAL_TICKET),
                      OrderValue(cnt,VAL_OPENPRICE),
                      x_1_up + (2 * point),
                      OrderValue(cnt,VAL_TAKEPROFIT),
                      BLUE);
          Exit;
        };
      };

      // if Stop Loss < Open Price then Set Takeprofit 

      if OrderValue(cnt,VAL_STOPLOSS) <= OrderValue(cnt,VAL_OPENPRICE) then
      {
        ModifyOrder(OrderValue(cnt,VAL_TICKET),
                    OrderValue(cnt,VAL_OPENPRICE),
                    OrderValue(cnt,VAL_STOPLOSS),
                    Bid - TakeProfit * Point,
                    BLUE);
        Exit;
      };
    };  // end OP_SELL check
  }; // end Symbol check
}; // end for cnt=1 to TotalTrades


 
Made an archive of 10 unprocessed photos, but it was too big (over 6MB), so I'll probably post it later. I did edit one page on this subject though:<br / translate="no">


There is a rather serious inaccuracy in the postulates stated in the book (as far as I can see from the published page) (IMHO: misunderstanding of the essence of the process). The point is that PRICE IS NOT A FUNCTION OF TIME. At any rate, it is impossible to prove it conclusively.
In that statement that I have described, the approach is built on the assumption that it is impossible to define reliably a function of what parameter the price is. Another assumption is that the price is a function of a superposition of external factors. We are trying to approximate changes in price and relate them to changes in time which is not the same thing. In other words, time is not an independent (variable) variable, it depends on several factors. It means some internal time of the system at the moment of which the event takes place. An external observer observing all this from outside in its system of coordinates can draw absolutely incorrect conclusions. For example: we stand on a road and count the number of cars that have passed in either direction. Of course on the basis of some information we can say that the number of cars passing on the track is a function of time but is it so? I specially gave an example for which the absurdity is obvious. Everything is more complicated here ;).

Regards, Vladislav.
Good luck and happy trends.