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 10.54% per annum.
- SBUX price at the close of May 20, 2024 was $77.54 and was lower than the bottom border of the primary price channel by $5.16 (6.24%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 36.22% per annum.
- SBUX price at the close of May 20, 2024 was inside the secondary price channel.
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 SBUX 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: January 4, 2023
End date: April 30, 2024
a = 5.0453
b = -0.0003
s = 0.0366
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0366) – 1
= 15.75%
January 4, 2023 calculations
Top border of price channel:
Exp(Y913)
= Exp(a + b × X913 + 2 × s)
= Exp(a + b × 1,324 + 2 × s)
= Exp(5.0453 + -0.0003 × 1,324 + 2 × 0.0366)
= Exp(4.7146)
= $111.56
Bottom border of price channel:
Exp(Y913)
= Exp(a + b × X913 – 2 × s)
= Exp(a + b × 1,324 – 2 × s)
= Exp(5.0453 + -0.0003 × 1,324 – 2 × 0.0366)
= Exp(4.5683)
= $96.38
April 30, 2024 calculations
Top border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 + 2 × s)
= Exp(a + b × 1,806 + 2 × s)
= Exp(5.0453 + -0.0003 × 1,806 + 2 × 0.0366)
= Exp(4.5676)
= $96.31
Bottom border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 – 2 × s)
= Exp(a + b × 1,806 – 2 × s)
= Exp(5.0453 + -0.0003 × 1,806 – 2 × 0.0366)
= Exp(4.4213)
= $83.20
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.54% per annum.
- SBUX price at the close of May 20, 2024 was $77.54 and was lower than the bottom border of the primary price channel by $5.16 (6.24%).
Secondary Trend
Start date: November 3, 2023
End date: May 20, 2024
a = 6.6397
b = -0.0012
s = 0.0430
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0012) – 1
= -36.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0430) – 1
= 18.77%
November 3, 2023 calculations
Top border of price channel:
Exp(Y1,123)
= Exp(a + b × X1,123 + 2 × s)
= Exp(a + b × 1,627 + 2 × s)
= Exp(6.6397 + -0.0012 × 1,627 + 2 × 0.0430)
= Exp(4.7208)
= $112.26
Bottom border of price channel:
Exp(Y1,123)
= Exp(a + b × X1,123 – 2 × s)
= Exp(a + b × 1,627 – 2 × s)
= Exp(6.6397 + -0.0012 × 1,627 – 2 × 0.0430)
= Exp(4.5487)
= $94.51
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(6.6397 + -0.0012 × 1,826 + 2 × 0.0430)
= Exp(4.4755)
= $87.84
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.6397 + -0.0012 × 1,826 – 2 × 0.0430)
= Exp(4.3035)
= $73.96
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 36.22% per annum.
- SBUX price at the close of May 20, 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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