//
// This AFL is intended to be used with any Price Data and if available CPI data
//
// If a symbol for CPI has been supplied then constant dollar plots will be shown
//        The CPI data should not be less granular then the chart periodicity
//
// This AFL will produce results beginning with the second bar
//
// Bars Offset can be used to align the beginning of the cycle wherever one wants
//
//        For example if the object was to see the presidential ( 4 year ) cycle
//
//        Using weekly data that began 9/1/1988 
//
//        You would set CycleLength to 208 i.e. 52 Weeks / Year * 4 Years
//
//        The first bar plotted would be for the week ending 9/2/1988
//
//        In order to align this to where the presidential cycle begins i.e. 1/1/1989,
//           one would change the Bars Offset to 17 to push the cycle plot ahead by 17 weeks
//
// Offset Cycles will position the plot under the specific occurance of the cycle
//        A value of 0 ( Default ) will position the plot at the beginning of the last cycle 
//        in the data and will show the extrapolation into future dates for as many bars 
//        as you have defined in the AB Preferences
//
// Separators are used to place vertical separators on the plot every n-bars.  In the above 
//        this would be set to 52 to show the different years in the weekly data of the 
//        presidential cycle
//
// GraphXSpace can be used to add extra space to the top and bottom of the plot
//
// RescalePrice = Yes will rescale the price data to the computed cycle ( usually not necessary )

CycleLength  = Param("Cycle Length",              208,  2, 10000, 1);
OffsetBars   = Param("Offset Bars",                17,  0, 10000, 1);
OffsetCycles = Param("Shift Cycles",                0,  0,  1000, 1);
Separators   = Param("Separators Every ? Bars",    52,  0,   100, 1);
GraphXSpace  = Param("GraphXSpace",                 5,  0,   100, 1); 
RescalePrice = ParamList("Rescale Price ?", "No|Yes");
SpecialData  = ParamList("Year in Vol AND Month in OI ?", "No|Yes");

CPISym       = "";//"CNPI-";//"CPI_1800";

OffsetBars   = OffsetBars + CycleLength;
OffsetCycles = OffsetCycles - 1;


Cum1    = Cum(1) - 1;
LVC1    = LastValue(Cum1);

if (OffsetCycles < 0)
    OffsetCycles = int(LVC1 / CycleLength);
    if (OffsetCycles < 0)
        OffsetCycles = 0;

Index   = IIf(BarIndex() == 0, L, IIf(L < Ref(L, -1), L, IIf(H > Ref(H, -1), H, C)));

if (SpecialData == "Yes")
{
    YYYY = V;
    MM   = OI;
}
else
{
    YYYY = Year();
    MM   = Month();
}

YYYYMM  = 100 * YYYY + MM;

if (CPISym != "")
    CPI = Foreign(CPISym, "C");
else
    CPI = Cum(0) + 1;

IndexCD = Index / CPI;

ii  = IIf(Cum1 < OffsetBars + 1, 0, int((Cum1 - OffsetBars - 1) / CycleLength) * CycleLength + OffsetBars);
iii = BarsSince(ii != Ref(ii, -1)) + OffsetBars + 1;

Za  = Cum(0);
Zg  = Cum(0) + 1;
N   = Cum(0);

for (i = OffsetBars + 1; i < BarCount; i++)
{
    Y[i] = IndexCD[i] / IndexCD[ii[i]];

    Za[iii[i]] = Za[iii[i]] + Y[i];
    Zg[iii[i]] = Zg[iii[i]] * Y[i];

    N[iii[i]]  = N[iii[i]] + 1;
}

ZZa  = IIf(Cum1 >  OffsetBars AND 
           Cum1 <= CycleLength + OffsetBars, Za / N, -1e10);
ZZg  = IIf(Cum1 >  OffsetBars AND 
           Cum1 <= CycleLength + OffsetBars, Zg ^ (1 / N), -1e10);

ZZa[OffsetBars] = 1;
ZZg[OffsetBars] = 1;

ZZZa = NOT IsEmpty(Ref(ZZa, -1)) AND (BarsSince(IsEmpty(Ref(ZZa, -1)))) % Separators - 1 == 0;
ZZZg = NOT IsEmpty(Ref(ZZg, -1)) AND (BarsSince(IsEmpty(Ref(ZZg, -1)))) % Separators - 1 == 0;

Price = IIf(IsEmpty(Ref(ZZa, CycleLength)), -1e10, Ref(IndexCD, CycleLength * OffsetCycles));

PMult = LastValue(Highest(IIf(IsEmpty(Ref(Price, -1)) AND NOT IsEmpty(Price), 1 / Price, 0)));

Price = IIf(Cum1 > LVC1 - CycleLength * OffsetCycles, -1e10, Price * PMult);

if (RescalePrice == "Yes")
{
    Factor = log10(LastValue(Highest(ZZa))) / log10(LastValue(Highest(Price)));
    Price = Price ^ Factor;
}
   

MinPlot = LastValue(Min(Lowest(IIf(ZZa > 0, ZZa, 1)), Lowest(IIf(Price > 0, Price, 1))));
MaxPlot = LastValue(Max(Highest(ZZa), Highest(Price)));

Plot(MinPlot, "", colorDefault, styleNoDraw);
Plot(MaxPlot, "", colorDefault, styleNoDraw);

Plot(Ref(ZZg, CycleLength), "", colorRed,  styleThick, Null, Null, CycleLength * OffsetCycles);
Plot(Ref(ZZa, CycleLength), "", colorBlue, styleThick, Null, Null, CycleLength * OffsetCycles);
Plot(Price, "", colorBrightGreen, styleThick, Null, Null, CycleLength * OffsetCycles);

Plot(IIf(Ref(ZZZa, CycleLength), 2, 1), "", colorLightBlue, styleHistogram | styleNoLabel | styleOwnScale, 1, 2, CycleLength * OffsetCycles);

if (Separators > 0)
    for (i = 1; i <= int(CycleLength / Separators); i++)
    {
        PlotText(NumToStr(i, 1.0), CycleLength * OffsetCycles + OffsetBars + int((i - 0.5) * Separators) - CycleLength + 1, MinPlot, colorWhite);
    }

Title = "Cycle Number = " + EncodeColor(colorWhite)       + NumToStr(OffsetCycles + 1, 1.0)                                       + "   " + EncodeColor(colorLightBlue) + 
        "Cycle Length = " + EncodeColor(colorWhite)       + NumToStr(CycleLength, 1.0)                                            + "   " + EncodeColor(colorLightBlue) + 
        "Price = "        + EncodeColor(colorBrightGreen) + NumToStr(Ref(Price, -CycleLength * OffsetCycles), 1.3)                + "   " + EncodeColor(colorLightBlue) + 
        "Geometric = "    + EncodeColor(colorRed)         + NumToStr(Ref(ZZg, - (CycleLength * OffsetCycles) + CycleLength), 1.3) + "   " + EncodeColor(colorLightBlue) + 
        "Arithmetic = "   + EncodeColor(colorBlue)        + NumToStr(Ref(ZZa, - (CycleLength * OffsetCycles) + CycleLength), 1.3);

SetOption("NoDefaultColumns", True);

Filter = 1;
AddColumn(YYYY,    "YYYY",     1.0);
AddColumn(MM,      "MM",       1.0);
AddColumn(YYYYMM,  "YYYY-MM",  1.0);
AddColumn(Cum1,    "Cum1",     1.0);
AddColumn(Index,   "Index",    1.5);
AddColumn(CPI,     "CPI",      1.5);
AddColumn(IndexCD, "Index CD", 1.5);
AddColumn(ii,      "ii",       1.0);
AddColumn(Y,       "Y",        1.5);
AddColumn(iii,     "iii",      1.0);
AddColumn(Za,      "Za",       1.5);
AddColumn(N,       "N",        1.0);
AddColumn(ZZa,     "ZZa",      1.5);
AddColumn(PMult,   "PMult",    1.5);