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 14.97% per annum.
- SBUX price at the close of November 19, 2024 was $98.35 and was higher than the top border of the primary price channel by $12.63 (14.74%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 87.83% per annum.
- SBUX price at the close of November 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 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: November 23, 2022
End date: August 12, 2024
a = 5.1472
b = -0.0004
s = 0.0577
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -14.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0577) – 1
= 25.94%
November 23, 2022 calculations
Top border of price channel:
Exp(Y758)
= Exp(a + b × X758 + 2 × s)
= Exp(a + b × 1,099 + 2 × s)
= Exp(5.1472 + -0.0004 × 1,099 + 2 × 0.0577)
= Exp(4.7742)
= $118.41
Bottom border of price channel:
Exp(Y758)
= Exp(a + b × X758 – 2 × s)
= Exp(a + b × 1,099 – 2 × s)
= Exp(5.1472 + -0.0004 × 1,099 – 2 × 0.0577)
= Exp(4.5435)
= $94.02
August 12, 2024 calculations
Top border of price channel:
Exp(Y1,187)
= Exp(a + b × X1,187 + 2 × s)
= Exp(a + b × 1,727 + 2 × s)
= Exp(5.1472 + -0.0004 × 1,727 + 2 × 0.0577)
= Exp(4.4951)
= $89.57
Bottom border of price channel:
Exp(Y1,187)
= Exp(a + b × X1,187 – 2 × s)
= Exp(a + b × 1,727 – 2 × s)
= Exp(5.1472 + -0.0004 × 1,727 – 2 × 0.0577)
= Exp(4.2644)
= $71.12
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 14.97% per annum.
- SBUX price at the close of November 19, 2024 was $98.35 and was higher than the top border of the primary price channel by $12.63 (14.74%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 1, 2024
End date: November 19, 2024
a = 1.4629
b = 0.0017
s = 0.0618
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 87.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0618) – 1
= 28.04%
May 1, 2024 calculations
Top border of price channel:
Exp(Y1,117)
= Exp(a + b × X1,117 + 2 × s)
= Exp(a + b × 1,624 + 2 × s)
= Exp(1.4629 + 0.0017 × 1,624 + 2 × 0.0618)
= Exp(4.3912)
= $80.74
Bottom border of price channel:
Exp(Y1,117)
= Exp(a + b × X1,117 – 2 × s)
= Exp(a + b × 1,624 – 2 × s)
= Exp(1.4629 + 0.0017 × 1,624 – 2 × 0.0618)
= Exp(4.1440)
= $63.06
November 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(1.4629 + 0.0017 × 1,826 + 2 × 0.0618)
= Exp(4.7401)
= $114.44
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.4629 + 0.0017 × 1,826 – 2 × 0.0618)
= Exp(4.4929)
= $89.38
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 87.83% per annum.
- SBUX price at the close of November 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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