/// <summary> /// 峰度 /// </summary> // = "sample" func Kurtosis(Ra *utils.SlidingWindow) (float64, error) { if Ra == nil || Ra.Count() <= 3 { return math.NaN(), errors.New("In Kurtosis, Ra == nil || Ra.Count() <= 3") } n := float64(Ra.Count()) method := "sample_excess" switch method { case "sample_excess": //kurtosis = sum((x-mean(x))^4/var(x)^2)*n*(n+1)/((n-1)*(n-2)*(n-3)) - 3*(n-1)^2/((n-2)*(n-3)) var_data, err := Variance(Ra) if err != nil { return math.NaN(), err } add_Sliding, err := utils.Add(-Ra.Average(), Ra) if err != nil { return math.NaN(), err } pow_Sliding, err := utils.Power(add_Sliding, 4.0) if err != nil { return math.NaN(), err } multi_Sliding, err := utils.Multi(1.0/math.Pow(var_data, 2.0), pow_Sliding) if err != nil { return math.NaN(), err } return multi_Sliding.Sum()*n*(n+1.0)/((n-1.0)*(n-2.0)*(n-3.0)) - 3*(n-1.0)*(n-1.0)/((n-2.0)*(n-3.0)), nil default: return math.NaN(), errors.New("In Kurtosis, method is default") } return math.NaN(), nil }
/// <summary> /// 偏度 /// </summary> // default = "moment" func Skewness(Ra *utils.SlidingWindow) (float64, error) { if Ra == nil || Ra.Count() <= 2 { return math.NaN(), errors.New("In Skewness, Ra == nil || Ra.Count() <= 2") } n := float64(Ra.Count()) method := "moment" switch method { //"moment", "fisher", "sample" case "moment": //skewness = sum((x-mean(x))^3/sqrt(var(x)*(n-1)/n)^3)/length(x) var_data, err := Variance(Ra) if err != nil { return math.NaN(), err } add_Sliding, err := utils.Add(-Ra.Average(), Ra) if err != nil { return math.NaN(), err } pow_Sliding, err := utils.Power(add_Sliding, 3.0) if err != nil { return math.NaN(), err } multi_Sliding, err := utils.Multi(1.0/math.Pow(var_data*(n-1.0)/n, 1.5), pow_Sliding) if err != nil { return math.NaN(), err } return multi_Sliding.Sum() / n, nil default: return math.NaN(), errors.New("In Skewness, method is default") } return math.NaN(), nil }
/// <summary> /// epsilon与R中不同,但似乎没有影响 /// Specific risk is the standard deviation of the error term in the /// regression equation. /// </summary> func SpecificRisk(Ra *utils.SlidingWindow, Rb *utils.SlidingWindow, scale float64, Rf float64) (float64, error) { //Period = Frequency(Ra) alpha, err := Alpha2(Ra, Rb, Rf) if err != nil { return math.NaN(), err } beta, err := Beta2(Ra, Rb, Rf) if err != nil { return math.NaN(), err } add_Ra_Sliding, err := utils.Add(-Rf, Ra) if err != nil { return math.NaN(), err } add_Rb_Sliding, err := utils.Add(-Rf, Rb) if err != nil { return math.NaN(), err } multi_beta_Slidinig, err := utils.Multi(beta, add_Rb_Sliding) if err != nil { return math.NaN(), err } sub_Ra_Beta, err := utils.Sub(add_Ra_Sliding, multi_beta_Slidinig) if err != nil { return math.NaN(), err } epsilon, err := utils.Add(-alpha, sub_Ra_Beta) if err != nil { return math.NaN(), err } var_eps, err := Variance(epsilon) if err != nil { return math.NaN(), err } var result = math.Sqrt(var_eps*float64(epsilon.Count()-1)/float64(epsilon.Count())) * math.Sqrt(float64(scale)) return result, nil }
/// <summary> /// Upside Risk is the similar of semideviation taking the return above the /// Minimum Acceptable Return instead of using the mean return or zero. /// (一般来说,非对称类的比较,单求此统计量意义有限) /// </summary> func UpsideRisk(Ra *utils.SlidingWindow, MAR float64, stat string) (float64, error) { r, err := utils.AboveValue(Ra, MAR) if err != nil { return math.NaN(), err } var length float64 method := "subset" switch method { case "full": length = float64(Ra.Count()) break case "subset": length = float64(r.Count()) break default: return math.NaN(), errors.New("In Upside Risk, method is default !!!") } if length <= 0 { return 0, nil } var result float64 switch stat { case "risk": add_Sliding, err := utils.Add(-MAR, r) if err != nil { return math.NaN(), err } pow_Sliding, err := utils.Power(add_Sliding, 2.0) if err != nil { return math.NaN(), err } multi_Sliding, err := utils.Multi(1.0/length, pow_Sliding) if err != nil { return math.NaN(), err } result = math.Sqrt(multi_Sliding.Sum()) break case "variance": add_Sliding, err := utils.Add(-MAR, r) if err != nil { return math.NaN(), err } pow_Sliding, err := utils.Power(add_Sliding, 2.0) if err != nil { return math.NaN(), err } multi_Sliding, err := utils.Multi(1.0/length, pow_Sliding) if err != nil { return math.NaN(), err } result = multi_Sliding.Sum() break case "potential": add_Sliding, err := utils.Add(-MAR, r) if err != nil { return math.NaN(), err } multi_Slding, err := utils.Multi(1.0/length, add_Sliding) if err != nil { return math.NaN(), err } result = multi_Slding.Sum() break default: return math.NaN(), errors.New("In UpSide Risk, method is default !!!") } return result, nil }
/// <summary> /// Appraisal ratio is the Jensen's alpha adjusted for specific risk. The numerator /// is divided by specific risk instead of total risk. /// </summary> func AppraisalRatio(Ra *utils.SlidingWindow, Rb *utils.SlidingWindow, scale float64, Rf float64, method string) (float64, error) { var result = 0.0 switch method { case "appraisal": be_data, err := Beta2(Ra, Rb, Rf) if err != nil { return math.NaN(), err } multi_Sliding, err := utils.Multi(be_data, Rb) if err != nil { return math.NaN(), err } sub_Sliding, err := utils.Sub(Ra, multi_Sliding) if err != nil { return math.NaN(), err } al_data, err := Alpha2(Ra, Rb, Rf) if err != nil { return math.NaN(), err } epsilon, err := utils.Add(-al_data, sub_Sliding) if err != nil { return math.NaN(), err } add_Sliding, err := utils.Add(-epsilon.Average(), epsilon) if err != nil { return math.NaN(), err } pow_Sliding, err := utils.Power(add_Sliding, 2) if err != nil { return math.NaN(), err } specifikRisk := math.Sqrt(pow_Sliding.Sum()/float64(epsilon.Count())) * math.Sqrt(float64(scale)) jsa_data, err := JensenAlpha2(Ra, Rb, Rf, scale) if err != nil { return math.NaN(), err } result = jsa_data / specifikRisk break case "modified": jsa2_data, err := JensenAlpha2(Ra, Rb, Rf, scale) if err != nil { return math.NaN(), err } be2_data, err := Beta2(Ra, Rb, Rf) if err != nil { return math.NaN(), err } result = jsa2_data / be2_data break case "alternative": jsa2_data, err := JensenAlpha2(Ra, Rb, Rf, scale) if err != nil { return math.NaN(), err } sr_data, err := SystematicRisk(Ra, Rb, scale, Rf) if err != nil { return math.NaN(), err } result = jsa2_data / sr_data break default: return math.NaN(), errors.New("In AppraisalRatio, method is default !!!") } return result, nil }