Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 13.10% per annum.
- PAYC price at the close of November 2, 2023 was $162.66 and was lower than the bottom border of the primary price channel by $53.14 (24.63%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 66.80% per annum.
- PAYC price at the close of November 2, 2023 was lower than the bottom border of the secondary price channel by $53.65 (24.80%).
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of PAYC price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 12, 2020
End date: October 31, 2023
a = 6.3368
b = -0.0004
s = 0.1305
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -13.10%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1305) – 1
= 68.54%
October 12, 2020 calculations
Top border of price channel:
Exp(Y486)
= Exp(a + b × X486 + 2 × s)
= Exp(a + b × 707 + 2 × s)
= Exp(6.3368 + -0.0004 × 707 + 2 × 0.1305)
= Exp(6.3258)
= $558.78
Bottom border of price channel:
Exp(Y486)
= Exp(a + b × X486 – 2 × s)
= Exp(a + b × 707 – 2 × s)
= Exp(6.3368 + -0.0004 × 707 – 2 × 0.1305)
= Exp(5.8037)
= $331.54
October 31, 2023 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(6.3368 + -0.0004 × 1,821 + 2 × 0.1305)
= Exp(5.8972)
= $364.00
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(6.3368 + -0.0004 × 1,821 – 2 × 0.1305)
= Exp(5.3751)
= $215.97
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 13.10% per annum.
- PAYC price at the close of November 2, 2023 was $162.66 and was lower than the bottom border of the primary price channel by $53.14 (24.63%).
Secondary Trend
Start date: July 6, 2023
End date: October 31, 2023
a = 10.9974
b = -0.0030
s = 0.0568
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0030) – 1
= -66.80%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0568) – 1
= 25.51%
July 6, 2023 calculations
Top border of price channel:
Exp(Y1,172)
= Exp(a + b × X1,172 + 2 × s)
= Exp(a + b × 1,704 + 2 × s)
= Exp(10.9974 + -0.0030 × 1,704 + 2 × 0.0568)
= Exp(5.9634)
= $388.94
Bottom border of price channel:
Exp(Y1,172)
= Exp(a + b × X1,172 – 2 × s)
= Exp(a + b × 1,704 – 2 × s)
= Exp(10.9974 + -0.0030 × 1,704 – 2 × 0.0568)
= Exp(5.7362)
= $309.88
October 31, 2023 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(10.9974 + -0.0030 × 1,821 + 2 × 0.0568)
= Exp(5.6100)
= $273.14
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(10.9974 + -0.0030 × 1,821 – 2 × 0.0568)
= Exp(5.3827)
= $217.62
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 66.80% per annum.
- PAYC price at the close of November 2, 2023 was lower than the bottom border of the secondary price channel by $53.65 (24.80%).
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