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 62.69% per annum.
- SBUX price at the close of April 2, 2025 was $99.41 and was lower than the bottom border of the primary price channel by $0.66 (0.66%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 71.65% per annum.
- SBUX price at the close of April 2, 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 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: May 1, 2024
End date: March 7, 2025
a = 2.3066
b = 0.0013
s = 0.0671
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 62.69%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0671) – 1
= 30.76%
May 1, 2024 calculations
Top border of price channel:
Exp(Y1,025)
= Exp(a + b × X1,025 + 2 × s)
= Exp(a + b × 1,489 + 2 × s)
= Exp(2.3066 + 0.0013 × 1,489 + 2 × 0.0671)
= Exp(4.4261)
= $83.61
Bottom border of price channel:
Exp(Y1,025)
= Exp(a + b × X1,025 – 2 × s)
= Exp(a + b × 1,489 – 2 × s)
= Exp(2.3066 + 0.0013 × 1,489 – 2 × 0.0671)
= Exp(4.1579)
= $63.94
March 7, 2025 calculations
Top border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 + 2 × s)
= Exp(a + b × 1,799 + 2 × s)
= Exp(2.3066 + 0.0013 × 1,799 + 2 × 0.0671)
= Exp(4.8395)
= $126.40
Bottom border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 – 2 × s)
= Exp(a + b × 1,799 – 2 × s)
= Exp(2.3066 + 0.0013 × 1,799 – 2 × 0.0671)
= Exp(4.5712)
= $96.66
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 62.69% per annum.
- SBUX price at the close of April 2, 2025 was $99.41 and was lower than the bottom border of the primary price channel by $0.66 (0.66%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 5, 2025
End date: April 2, 2025
a = 10.8671
b = -0.0035
s = 0.0375
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0035) – 1
= -71.65%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0375) – 1
= 16.19%
February 5, 2025 calculations
Top border of price channel:
Exp(Y1,216)
= Exp(a + b × X1,216 + 2 × s)
= Exp(a + b × 1,769 + 2 × s)
= Exp(10.8671 + -0.0035 × 1,769 + 2 × 0.0375)
= Exp(4.8328)
= $125.57
Bottom border of price channel:
Exp(Y1,216)
= Exp(a + b × X1,216 – 2 × s)
= Exp(a + b × 1,769 – 2 × s)
= Exp(10.8671 + -0.0035 × 1,769 – 2 × 0.0375)
= Exp(4.6828)
= $108.07
April 2, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(10.8671 + -0.0035 × 1,825 + 2 × 0.0375)
= Exp(4.6394)
= $103.49
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(10.8671 + -0.0035 × 1,825 – 2 × 0.0375)
= Exp(4.4894)
= $89.07
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 71.65% per annum.
- SBUX price at the close of April 2, 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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