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 211.64% per annum.
- LULU price at the close of February 20, 2025 was $365.82 and was lower than the bottom border of the primary price channel by $32.65 (8.19%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 92.19% per annum.
- LULU price at the close of February 20, 2025 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 LULU 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: August 1, 2024
End date: February 11, 2025
a = 0.3955
b = 0.0031
s = 0.0472
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0031) – 1
= 211.64%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0472) – 1
= 20.79%
August 1, 2024 calculations
Top border of price channel:
Exp(Y1,118)
= Exp(a + b × X1,118 + 2 × s)
= Exp(a + b × 1,623 + 2 × s)
= Exp(0.3955 + 0.0031 × 1,623 + 2 × 0.0472)
= Exp(5.5443)
= $255.78
Bottom border of price channel:
Exp(Y1,118)
= Exp(a + b × X1,118 – 2 × s)
= Exp(a + b × 1,623 – 2 × s)
= Exp(0.3955 + 0.0031 × 1,623 – 2 × 0.0472)
= Exp(5.3554)
= $211.76
February 11, 2025 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,817 + 2 × s)
= Exp(0.3955 + 0.0031 × 1,817 + 2 × 0.0472)
= Exp(6.1485)
= $468.00
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,817 – 2 × s)
= Exp(0.3955 + 0.0031 × 1,817 – 2 × 0.0472)
= Exp(5.9596)
= $387.45
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 211.64% per annum.
- LULU price at the close of February 20, 2025 was $365.82 and was lower than the bottom border of the primary price channel by $32.65 (8.19%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 30, 2025
End date: February 20, 2025
a = 18.6611
b = -0.0070
s = 0.0179
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0070) – 1
= -92.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0179) – 1
= 7.41%
January 30, 2025 calculations
Top border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 + 2 × s)
= Exp(a + b × 1,805 + 2 × s)
= Exp(18.6611 + -0.0070 × 1,805 + 2 × 0.0179)
= Exp(6.0886)
= $440.82
Bottom border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 – 2 × s)
= Exp(a + b × 1,805 – 2 × s)
= Exp(18.6611 + -0.0070 × 1,805 – 2 × 0.0179)
= Exp(6.0171)
= $410.39
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(18.6611 + -0.0070 × 1,826 + 2 × 0.0179)
= Exp(5.9420)
= $380.68
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(18.6611 + -0.0070 × 1,826 – 2 × 0.0179)
= Exp(5.8704)
= $354.40
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 92.19% per annum.
- LULU price at the close of February 20, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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