Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 30.13% per annum.
- DLTR price at the close of November 22, 2022 was $152.37 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 11.51% per annum.
- DLTR price at the close of November 22, 2022 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 DLTR 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: February 25, 2020
End date: November 22, 2022
a = 3.7798
b = 0.0007
s = 0.1098
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 30.13%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1098) – 1
= 55.15%
February 25, 2020 calculations
Top border of price channel:
Exp(Y564)
= Exp(a + b × X564 + 2 × s)
= Exp(a + b × 823 + 2 × s)
= Exp(3.7798 + 0.0007 × 823 + 2 × 0.1098)
= Exp(4.5933)
= $98.82
Bottom border of price channel:
Exp(Y564)
= Exp(a + b × X564 – 2 × s)
= Exp(a + b × 823 – 2 × s)
= Exp(3.7798 + 0.0007 × 823 – 2 × 0.1098)
= Exp(4.1541)
= $63.69
November 22, 2022 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.7798 + 0.0007 × 1,824 + 2 × 0.1098)
= Exp(5.3155)
= $203.47
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.7798 + 0.0007 × 1,824 – 2 × 0.1098)
= Exp(4.8763)
= $131.15
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 30.13% per annum.
- DLTR price at the close of November 22, 2022 was $152.37 and was inside the primary price channel.
Secondary Trend
Start date: March 16, 2022
End date: November 22, 2022
a = 5.6153
b = -0.0003
s = 0.0720
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -11.51%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0720) – 1
= 33.40%
March 16, 2022 calculations
Top border of price channel:
Exp(Y1,083)
= Exp(a + b × X1,083 + 2 × s)
= Exp(a + b × 1,573 + 2 × s)
= Exp(5.6153 + -0.0003 × 1,573 + 2 × 0.0720)
= Exp(5.2325)
= $187.26
Bottom border of price channel:
Exp(Y1,083)
= Exp(a + b × X1,083 – 2 × s)
= Exp(a + b × 1,573 – 2 × s)
= Exp(5.6153 + -0.0003 × 1,573 – 2 × 0.0720)
= Exp(4.9443)
= $140.38
November 22, 2022 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.6153 + -0.0003 × 1,824 + 2 × 0.0720)
= Exp(5.1484)
= $172.16
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.6153 + -0.0003 × 1,824 – 2 × 0.0720)
= Exp(4.8603)
= $129.06
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 11.51% per annum.
- DLTR price at the close of November 22, 2022 was inside the secondary price channel.
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