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 66.45% per annum.
- LULU price at the close of September 19, 2024 was $270.76 and was higher than the top border of the primary price channel by $9.82 (3.76%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 117.25% per annum.
- LULU price at the close of September 19, 2024 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: December 11, 2023
End date: September 12, 2024
a = 10.9120
b = -0.0030
s = 0.0578
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0030) – 1
= -66.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0578) – 1
= 26.00%
December 11, 2023 calculations
Top border of price channel:
Exp(Y1,063)
= Exp(a + b × X1,063 + 2 × s)
= Exp(a + b × 1,543 + 2 × s)
= Exp(10.9120 + -0.0030 × 1,543 + 2 × 0.0578)
= Exp(6.4110)
= $608.51
Bottom border of price channel:
Exp(Y1,063)
= Exp(a + b × X1,063 – 2 × s)
= Exp(a + b × 1,543 – 2 × s)
= Exp(10.9120 + -0.0030 × 1,543 – 2 × 0.0578)
= Exp(6.1799)
= $482.95
September 12, 2024 calculations
Top border of price channel:
Exp(Y1,252)
= Exp(a + b × X1,252 + 2 × s)
= Exp(a + b × 1,819 + 2 × s)
= Exp(10.9120 + -0.0030 × 1,819 + 2 × 0.0578)
= Exp(5.5852)
= $266.47
Bottom border of price channel:
Exp(Y1,252)
= Exp(a + b × X1,252 – 2 × s)
= Exp(a + b × 1,819 – 2 × s)
= Exp(10.9120 + -0.0030 × 1,819 – 2 × 0.0578)
= Exp(5.3541)
= $211.48
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 66.45% per annum.
- LULU price at the close of September 19, 2024 was $270.76 and was higher than the top border of the primary price channel by $9.82 (3.76%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: August 1, 2024
End date: September 19, 2024
a = 1.7095
b = 0.0021
s = 0.0351
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 117.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0351) – 1
= 15.07%
August 1, 2024 calculations
Top border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 + 2 × s)
= Exp(a + b × 1,777 + 2 × s)
= Exp(1.7095 + 0.0021 × 1,777 + 2 × 0.0351)
= Exp(5.5571)
= $259.06
Bottom border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 – 2 × s)
= Exp(a + b × 1,777 – 2 × s)
= Exp(1.7095 + 0.0021 × 1,777 – 2 × 0.0351)
= Exp(5.4167)
= $225.12
September 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.7095 + 0.0021 × 1,826 + 2 × 0.0351)
= Exp(5.6612)
= $287.50
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.7095 + 0.0021 × 1,826 – 2 × 0.0351)
= Exp(5.5208)
= $249.84
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 117.25% per annum.
- LULU price at the close of September 19, 2024 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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