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 12.19% per annum.
- SBUX price at the close of April 18, 2024 was $87.15 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 29.35% per annum.
- SBUX price at the close of April 18, 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 18, 2024
a = 5.1564
b = -0.0004
s = 0.0367
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -12.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0367) – 1
= 15.80%
January 4, 2023 calculations
Top border of price channel:
Exp(Y934)
= Exp(a + b × X934 + 2 × s)
= Exp(a + b × 1,353 + 2 × s)
= Exp(5.1564 + -0.0004 × 1,353 + 2 × 0.0367)
= Exp(4.7478)
= $115.33
Bottom border of price channel:
Exp(Y934)
= Exp(a + b × X934 – 2 × s)
= Exp(a + b × 1,353 – 2 × s)
= Exp(5.1564 + -0.0004 × 1,353 – 2 × 0.0367)
= Exp(4.6011)
= $99.59
April 18, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.1564 + -0.0004 × 1,823 + 2 × 0.0367)
= Exp(4.5804)
= $97.55
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.1564 + -0.0004 × 1,823 – 2 × 0.0367)
= Exp(4.4337)
= $84.24
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 12.19% per annum.
- SBUX price at the close of April 18, 2024 was $87.15 and was inside the primary price channel.
Secondary Trend
Start date: November 3, 2023
End date: April 18, 2024
a = 6.2059
b = -0.0010
s = 0.0235
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -29.35%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0235) – 1
= 9.84%
November 3, 2023 calculations
Top border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 + 2 × s)
= Exp(a + b × 1,656 + 2 × s)
= Exp(6.2059 + -0.0010 × 1,656 + 2 × 0.0235)
= Exp(4.6764)
= $107.39
Bottom border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 – 2 × s)
= Exp(a + b × 1,656 – 2 × s)
= Exp(6.2059 + -0.0010 × 1,656 – 2 × 0.0235)
= Exp(4.5826)
= $97.77
April 18, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(6.2059 + -0.0010 × 1,823 + 2 × 0.0235)
= Exp(4.5175)
= $91.60
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.2059 + -0.0010 × 1,823 – 2 × 0.0235)
= Exp(4.4236)
= $83.40
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 29.35% per annum.
- SBUX price at the close of April 18, 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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